Is there an easy trans linkage adjustment for this?

[89Vette]

Mine won't start in neutral (w/o wiggling the selector handle). I also discovered my backup lights don't always light-up. I'm thinking there must be a cable under the console that I can adjust (just a hair) to reliably engage these functions?

Also, occasionally, I get a slight oscillating (shimey) of the front wheels. Oddly, I only notice it when cold...and about the same place. The road surface might contribute but it's like when my old Grand Cherokee had a bad steering stabilizer (shock). I think I looked a while back and didn't see such a part installed on the Isuzu. Any ideas what could cause this? With new tires unlikely to have balance issues. Plus, if they did, why only cold?

Maybe a slight about of play in the steering linkage that swells with use? Is there anything to laterally stabilize these truck's steering?