You can see A class availability on expert flyer into Premium Economy but you can’t see R class for business on expert flyer. I read some people call up to clear upgrades. I’ve had it clear pretty much immediately after booking without calling.
If you don’t have access to expert flyer and you’re after premium economy you can just go through the booking process. The website shows you in brackets if A class is available. Look for ‘deal’ or the purple triangles at the top of the boxes. They’ll likely have A class available. Then book and apply your upgrade. It should clear < 30mins. I never checked prior to 30mins.
If you’ve already booked and then find A class, you could call up and ask them to clear your upgrade. I’m not sure if it clears immediately if you have booked but wait for A class and then apply online.
Also with business class, if there is I class available I would call and see if they can clear your upgrade.
It’s not about how many seats you see on the seat maps, there have to be specific classes available to clear upgrades. They will process the upgrades closer the time and well, you really don’t know who else is in the queue or if they requested their upgrade earlier etc