Here is a little semi GMless game of inspectres that me and my roomie have started.The way it works is we roll up a client and from that frame work we say whatever ideas pop into our heads about the admix of circunstances and there we have a client! Next we role play out the interview, The way we work out NPCs is the person not currently playing their character plays the NPC, We also occasionally come up with ideas for NPCs to simply walk on stage during a jobe and throw them in.As for stress rolls, whenever something stressful happens we remind each other to roll, also, sometimes we will simply throw a stressor into a scene, but we try to limit that to keep from getting bogged down. The game is set in our home town of sacramento in a place that in our word is a closed down karate dojo. The Two employees of ITL have set up cubicle walls to make it look somewhat more like an office, the agents are

Eliana
Manager and Public Relations

Dresses in "Power Suits" and heels, trying to cultivate an image of the classic female business shark. She is a former marketing consultant and linguistics student

Academics: 3

Athletics:1

Technology:2

Contact: 3

Talent
Language

Robert
Finance, Research and technology department (he's not the head of the department, he is the dpetartment)

He wears a goatee and a ponytail and comes to work in just a t-shirt and jeans, he smells really strongly of incense

He is a computer tech with hobbies in invention and occultism, he is very excited that he has the resources of the franchise to expand his library of books devoted to his hobbies.

Academics:4

Athletics:1

Technology: 3

Contact: 1

Talent
Occultism

Our first case, We get a call from parks and Recreation, they send a man over who is frantic to clear two local parks of what seems like possessed squirrels. One particularly fun exchange was this,

Parks Guy: You guys have experience with this kinda stuff, right?
Elaina:Theres not much we don't have experience not with.
Parks Guy: Huh?

Confessional Moment
Robert: Sometimes I think the only reason Elaina is so persuasive is because she confuses people.

Elaina gains the confusing trait.

Two local parks have been infested by squirrels who seem emmaciated and have glowing eyes, anyone who goes farther than the sidewalk is immediately attacked, Parks and Rec needs this cleared up before the weekend when families will be going out.
We get ready to go to the park and do some investigating, Robert gets a six on a technology roll and decides we have an armored car, it is white with the name of the company on the side, and on either side of it the InSpectres logo and the all seeing eye. The back is set up to hold all kinds of equipment due to modular design, from surveilence to weapons and gadgets and even live specimens.
on the way to the park the dashboard camera catches this exchange,

Elaina:We should stop and get bagels.
Robert: You want to stop in the middle of a job for bagels?
Elaina: It's for the job, throw it in a trap and the squirrels will go for it.
Robert:You think demonic flesh eating squirrels are gonna want bagels?
Elaina: Oh... We should stop for ground beef.

Elaina spends a credit card point on a technology roll roll catch the squirrels and rolls a six. She ties rope around some humane racoon traps loaded with ground beef and tosses them into the park, it works and the squirrels swarm the traps, even biting each other to get at the beef. she pulls the traps in and then throws some beef into the forest to get the squirrels still clinging to the trap off.
They go back to HQ to examine their catch, Robert spends a library Card point and rolls academics and gets a six
It turns out the squirrels are possessed collectively by the spirit Olo-Chimbo, a desert spirit of starvation and desperation.
Elaina Rolls contact and gets a six on a bank die
She calls in one of her fathers friends, a college professor with occult experience to exorcise the spirit. He takes the cage of squirrels back to the park, he draws a circle in chalk around himself and the cage, he then pulls out a silver bowl and fills it with water. He chants as he mixes ground herbs and salt with the water before throwing it over the squirrels, there is an unearthly scream and a shockwave of light that knocks out anything electronic in a three block radius.

Exorcist: This place is clean.

We go to the other park, catch more squirrels with  five on a tech roll and repeat the same ritual with a six in contacts. Mission sucess!

Unfortunately we forgot about stress rolls so our franchise is growing a bit too fast, but that will be made up for in the next session hopefully.

oh, and if anyone has ideas on how to improve the GMless part of our system, please chime in.

I've always thought InSpectres was a game that was better suited to being GMless than to having a dedicated GM. I know I always flailed around when trying to GM it and trying to understand what it was I, as GM, was supposed to do or facilitate or whatnot. It seemed really that there wasn't anything I was necessary for, and that all having a GM did was screw with the dynamic of play (putting in an authority figure, and the expectations of what that meant, who really didn't need to be there).

After some play and consideration, I figured a floating GM "position" would have been a better design -- like the Dealer in a game of poker, or the Banker in Monopoly, where they're flat-out just another player, but also something extra when needed (and that the game can't end up centered around). Which I think you and your friend are doing by being one another's GMs back-and-forth in the same game.

Disclosure, I haven't read/played InSpectres in a couple years at this point, so the exact rules are a bit fuzzy now. As such, the only improvement I can think of off-hand is one that you appear to have noted yourself: for the GM to call for Stress rolls. There's a scene, there's some rolls, and then the GM can go: Stress roll!

Otherwise, cool game! I'd love to hear how the next sessions go.

I love Inspectres. Your variant seems just right for a two-player game, although I have generally been happy with the formal GM presence in my experience of the game (all with more than two players, usually a lot more).

I'm chiming in here to say that some kind of formalized Stress reminder may be useful to you. Something like a "Did you check for Stress?" step whenever you change scenes, and if you didn't when you should have, check it then. I'm even thinking of something cute and physical, an object (whatever it may be), that one person literally holds during a given scene, and then gives it to the other person at the start of the next scene, and that transfer could signal asking the question.

Best, Ron

P.S. H'mmm ... both agents with Athletics 1? That sounds like a cue for a very athletically-demanding situation in the next case ... potentially quite Stressful, eh?