20 - 25 seconds to turn on is BAD!
It's not the relay itself, but the underlying circuitry, most likely a bad electrolytic capacitor. You could check the DC on the outputs too (when the relay is engaged of course). If it is too much, do not adjust it before the rebuild.
Do you still use the 8088 on a daily basis? If so, check how much heat it generates, the cover should be a little warm to touch, but not hot. If it is hot, you'd for sure better not use it anymore before the rebuild.
The FL meters normally can be left alone, including the trimmer pots. Only if you notice strange behaviour - for instance; I once had one that always had one segment lit - you should adjust it.
And for the osicillator, not really a need for those anymore nowadays when you have a computer with a sound card or a smartphone with a tone generator app.
Here for instance you find an online tone generator;
http://onlinetonegenerator.com/
With the DMM on AC you can adjust the volume to the 0.75 Volt you will need for the adjustment of the 8088 (the 8077 might be the same).
Advise on replacing the relay; relays seldom or never go bad by themselves. The contacts can get burned if there are shorts or too much sparking (only when an amp is in bad condition already) or they can just be dirty. Of course a new relay will prevail any possible shortcoming and it is more convenient, since it will spare you the trouble and working with these pesky fibre glass pens. But it will save you some money servicing the old one and - for the real "vintage" aficionado's, the amp retains a more original look.
I never replace any of the other capacitors nor resistors if they are ok. And they will always be, unless perhaps they were at a spot where something went severly wrong. But even then for instance ceramic capacitors nearly always survive. Resistors is another thing, they can go up or down in resistance when stressed and fuse resistors can break down without showing any damage, but again, fortunately, Technics doesn't use these kind of little devils...