84 GSL-SE Doesn’t wanna start after driving a while
 

The fist thing I would do is a rotary specific compression test. Ensure you have a good base to start with.

Have you removed the plugs after the engine stalls to ensure they are still dry? A stuck fuel injector will cause stalling and flooding and the injectors on the GSL-SE's should be removed and cleaned if they have not already.

How old are the plugs, wires, cap, and rotor? Is the throttle position sensor in adjustment? Have you checked for any vacuum leaks?

Have you changed the fuel filters? There is one near the fuel pump. On the GSL-SE there is also a screen on one of the components on the fuel delivery system. Not sure where it is at.

https://cimg7.ibsrv.net/gimg/www.rx7...a51bf992a.jpeg
Car came like this. I have no idea why they did this. Does anyone knows? seems like the fuel supply line and the return are linked together

Prior owner installed a fuel pressure bleed-down kit. Basically, it allows for passage of high pressure feed linked to the return so that when you shut the car down, the pin holes between the two will create a path of least resistance to bleed pressure through the return back to the tank. It was used as a method to fix cars that would leak down pressure through an injector and flood the car. It works, but is not optimal.

on a properly tuned SE with good injectors it is not needed.

Easiest way to do that is to buy 2-3 ft of Fuel Injection Hose and pull off the Upper Intake Manifold which will allow you to remove the Feed and Return Lines from the Fuel Rail. Just replace both Feed and Return with new hose to the Feed & Return on the firewall, and you're done. You might want to hang onto the bypass setup as pictured above, as I'm betting the prior owner probably did that (*or paid to have it done) for a good reason. In other words, you might need to hook it back up if it behaves even worse after you configure it back to stock. Good luck,

Thanks!

Keep us updated with the results of converting it back to its original form.