One other thought while you've got it apart. I replaced the pinion gear on Bugsy my '68 Sprite while I had things apart. There are several pinion gears but the ones for '68, '69 were relatively cheap like < $10.00 when I reduild the front end 8-9 years ago. Later ones for the Triumph Rack are expensive but for the earlier racks again relatively cheap when I bought mine. It did appreciably reduce front end sway and play and improved steering feel. While you are in there renewing all other parts this is a might as well thing to do.
Remember to replace the bolt that attaches the column to the steering rack. This is a similar alignment fit like the trunion bolts. And use a steel locking nut on the end not a nylock.
Other tips, I replaced the rack bolts but make sure you've got the exact size. Those bolts bottom out and if bolts are too long rack clamps will not tighten properly and rack will be moving around all over the place. Clean out those holes with a bottoming tap, all sorts of crud gets in there. I lines both sides of the rack base and rack clamps with pieces of inner tube glued to the clamps. Ideally do only one side as this is where you get the ground for the horn through this connection.
Don't overtighten the rack bolts. That's aluminum you are bolting to and you don't want to strip things out.
Steering column upper fixing bolts 12-17 Ft/lbs
Steering column pinch bolt 9-12 Ft/lbs
Steering rack housing clamp bolts 20-22 Ft/lbs
Steering rack mounting bracket bolts 17-18 Ft/lbs
Tie rod ball joint nut 28-32 Ft/lbs
Tie rod end assembly locknut 30-35 Ft/lbs
Tie rod rack locknut 80 Ft/lbs
Hope this helps.