How wobbly is the teeter? These seats, being the age that they are, will all have some play. But even still, there shouldn't be an extreme amount of play unless there is a prob.
There's several things to check. They all involve pulling the seat back out.
-Are the tracks bolted tight to the bottom of the seat?
-Are the tracks tight to the uprights?
Seeing as you just installed them, I wouldn't think that the uprights to floor bolts would be loose.
If all that's good, then it's in the tracks themselves. That can be caused by a few things.
-The seats have been in an accicdent. The weight of even a fairly small person being thrown forward & then back into the seat can cause damage to any part of the seat. The seat frames, backrest hinges, tracks or the uprights.
-The seats were in a truck owned by a rather large person. Sometimes the damage caused by that can be the equivelent of an accident, but just occuring over a longer period.
The tracks consist of 2 slides that work in conjunction. The outer edges of the uppers wrap around the edges of the lowers. An accident or large person can cause the edges which wrap around to spread, creating play. You could try to tighten the edges up by a few whacks with a decent sized hammer down the length of those edges. That may or may not work. Don't bend the edges too much or the tracks won't work at all.
Inside the tracks are a couple of rollers. They can cause problems with excessive play. Most owners never check to see if there is enough grease in there for the rollers to roll on. The rollers push the grease out of the travel area over time. Once that happens, it's metal on metal & it's the rollers that take the brunt of that. No grease & they can stop rolling & are just sliding, creating a flat spot on the roller.
Also, the rollers can become jammed up inside the track. If this happens & one or the other is stuck towards the middle of the track, it becomes a pivot point.
GM tracks also have been known to actually spit a roller out. (2 per track.) At either end of the track is a stamped bump which is there to prevent such. It doesn't always work. Check to see if the tracks actually do have 2 rollers a piece.
Working on tracks can be a PitA. Sometimes it's easier to just pick up another set in better shape.
Did you replace a bench seat with this one? Did it have any play in the tracks? Any weeble/wobble? If not, then I'd just swap them over from the original seat to this new one.
With all that said...I love that style of seat you installed. I have several seats for 400's in the stash, from early style benches to early & late style buckets.
In 18 years or so of owning 400's, I've only ever found 2 of those benches. Because...Canada!
One was thrashed (Dog inhaled 75% of it!) & the other was (at the time, I thought) too expensive. $200.00. If I'd of known what I know now, I would of gladly coughed up that price!
I've been keeping my eyes open for one since. I don't care what shape it's in. The one the JYD's been sleeping on. Caught on fire & the only thing left is the frame. I don't care! I can make it purdy again!
Finding one of those seats is akin to finding a set of 454SS buckets. They just don't come up for sale around here.
Color me jealous!