Just bought this car

1989 Camaro

Car was parked in a garage for about 1.5 years. Test drove the car and it had a slight skip to it. would backfire on deceleration a little.

Paid for the car and it started to skip terrible. Put in fresh fuel and it would not start back up.

Car now starts but will not idle or rev up. It will backfire and spit fire from the tbi unit.

Changed fuel filter. Same problem.

I can spray carb cleaner and it runs perfect. (while spraying) Revs smooth. The fuel flow from the injectors seems good at idle when it does run but as soon as i give it fuel the pattern become very small.

Does this sound like the fuel pump?

 

Well I have a TPI and i'm not familiar with the TBI setup. However, from what you describe it does sound fuel related.
I would start with the basics before spending any £££. Just check everything is hooked up right, no vac leaks, melted plug wires etc. I've seen plenty of third gens here in the UK with bad home repair jobs, throttle position sensors missing bolts, idle control valves disconnected etc etc.
Having done a check round i'd make sure the engine management light is working (i.e the previous owner hasn't taken the bulb out in an effort to hide a fault. If there are any codes, pull them off with the paperclip trick.
I would also run a fuel pressure test, checking that the pump primes and builds up pressure quickly. I think you need to remove the tank OR cut an inspection hole in the trunk to access the pump.
I've bought three replacement fuel pumps in the past for various aging cars in all cases the problem was with something else. A few checks should help you make an informed decision. In any case, fitting a new pump is good insurance if your keeping the car