Hello Raphael,
You battery takes the charging. 12.7 V indicate you have a "liquid" (flooded) battery and that it arrives at 100 % charge. (if I'm wrong on the type of battery, please tell me).
The other figure is not good. It tells me that your battery has got to it's end of life. (a battery looses it's nominal capacity as it is used. At first it is 20 Ah, then it becomes a 15 Ah... and so on until it reaches 0 Ah).
It seems, given your figures above, that the battery has not enough capacity to supply the bike with ignition on, thus the voltage drops under 12V. With the ignition ON, you only power the ignition circuit, the tachometer and maybe the headlight if your bike has permanent light on. So the voltage should have stayed well above 12V, maybe 12.6 or even 12.7V.
Given that, it has not enough capacity to drive the starter motor which is a huge sucker. When you press the starter button you request your battery to give something around 300 A to the starter motor. This is a huge drain on the battery. So we expect that the voltage will drop to around 12V during the time the starter runs. Your battery drops to 6V ! half it's rated voltage ! So clearly, it collapse under the load and your starter motor has not enough juice to power it's internal relay (300 A is a huge current and need a huge relay to cope with).
If your battery is somewhat old you will have to replace it and go. If it is not, you will have to replace it and troubleshoot what has killed it on the bike. For peace of mind, after replacing the battery, we will check that everything's fine and you will learn how to check using your new multimeter.
But replacing the battery is/may be the first step.
I do not know where you live, but one can find relatively cheap AGM batteries suitable for the R65 and requiring no maintenance. There is an permanent thread on the upper part of this sub forum about that.
Have a nice day, even if it started not so good....