Either a bad battery or bad connection somewhere is my guess and not being able to do any actual tests, that all it is, a guess.
I use the analogy of you can have 9-1.5V C cells in series and they'll read 13.5V on multimeter but they don't have the capacity i.e. amperage to turn over the bike. I
believe that is your problem but not being able to load test it, it's just a guess. That's what you're going to have to do, get the battery load tested.
Think of it this way also. Lets say for arguments sake each cell of a 6 cell auto battery has 20 plates (random guess LOL) that generate 1.5V so you need each of those plates to contribute to the amperage output of each cell and each cell to contribute to the total of the battery. If only one or two plates of each cell is contributing you've got the voltage as each plate generates 1.5V but no amperage.
You may be able to watch the voltage on your meter as you turn the key to start and I'll bet it'll drop to close to zero but that's not just checking the battery alone, it's also checking the connections from the battery as well.
I've had batteries go bad on a tender, once the tender fried it as it went bonkers charging at 16V (Boiling batteries smell great, think rotten eggs

). The other the battery had lived a good live at 7-8 years and it was time.