The car is a 87 camaro 305 4bbl (H) Sport Coupe Berlineta (this must mean the tranny is A4)

I finally fixed the engine after the car had been standing for 2 years. When testing the engine on the street in front of the garage there seemed to be no problem with the transmission. However when I went on a larger road and whenever I got to 50mph the car would switch off gear and just rev. This would also happen when I'm climbing a small hill. Unless I stop or slow down to a really low speed the tranny wouldn't start shifting into gear. I think all this happens when I get to 3rd gear, but I'm not completely sure.
The last time I checked the oil level was right and the car hasn't been driven since then. Also last time I drove the car the tranny was ok, at least it shifted into gear.

These are the things that I've changed:
Rebuilt carb
MAP sensor
Coolant temp sender and sensor
ICM
Distr cap
Oxygen sensor
Plug wires

A thing that may be important is that I have no tail lights. They work, at least when the headlights are turned on.

Can you please tell what to check and where to start? I know nothing about this transmission. What controls it and tells it when to shift gear and lock up?

Does this sound like a problem inside the trans. or something that controls it?

Thank you.
I really thought my car was ready to go.

Sounds like bad tranny, soundsl ike it's slipping - might be time for a rebuild/replace.

But it can't break just by standing, can it?
What controls the transmission? Where should I look for the switch for the tail lights? Does it have any role in controlling the tranny?

its not an electrical problem you have because it not an electric shift trans for the most part. only the lock up converter is electric. did you adjust the tv cable correct? if its hooked up wrong/ adjusted wrong it will not shift correct and you should not drive it till it is fixed.

So it's the TV cable controlling the tranny? I believe there's a huge possibility it's not correctly adjusted.
I'll search for a thread on how to adjust it now.

So since I did drive the car with the TV cable not adjusted and I most probably fired the transmission. How do I confirm this sad fact? All I can think of is smelling the trans oil and checking its color.

adjust it correctly and see if its better. if so change the filter and fluid and be done with it. read everything about it before you adjust it. i find that if you push the tab then push the cable back in the sleeve then let go of the tab and open the throttle all the way { not running of course} that it seems to adjust nice and have good shifts. it will make a ratcheting sound. its ok to do that. shoulda seen the first time i heard that. i ran next store to the tranny shop and told the guy i broke the trans. lmfao.

Thank you. Do you know a good article on adjusting the TV cable on a carbed 305 or should I just search the forum?

Also, how do I identify my trans type? Is it the 700r4. The tech data on the main page says it should be A4. What's A4?

a4= automatic 4 speed. search. there are a bunch of articles on here. tech stuff on the main page even has it.

Ok, so the TV cable was set-up properly, but the transmission has been driven with low oil level, so as a result I now have no 3rd gear. It's clear that it is going for a rebiuld, but there's something more that bothers me. At 2nd and at 1700rpms the car shakes, at 2000 it runs smoother. What's broken and causes that? I wanna make sure the tranny guy fixes that too, not just the third gear.