Starter problems

Battery is only 2 months old m8 and fully charged and even when ignition on and button pressed still shows 13.03 volts

Just orded a solenoid from FleaBay so fingers crossed

Whilst we are on the subject of dodgy starting, I have a potential problem that has recently surfaced ..

Bike is a 99 curvy with 25 k on the clock. When I got it a couple of months ago, it started fine as far as I can recall.
lately if it has been standing a day or so, when I thumb the starter from cold, it really struggles to turn over the engine, and the starter seems to drop out after a few turns rather than keep turning. Lights dim,as though the battery is low on charge and after a couple of times it doesnt seem to have the power to turn at all (like a flat battery). If I leave it for a while (few minutes) it turns slowly but fires and starts (even with no choke), then runs fine.
When the engine is warm, seems to start OK, on the button immediately no worries.

But as I am planning a trip to france shortly, I dont wanna get stranded in some remote french spot ...

Had the battery off tonight and on the 20V Dc setting on a multimeter, was reading about 15.5, so plenty charge there ?
Any thoughts ? starter motor? Starter relay (solenoid?) ?
I changed the oil recently for new, and as far as I know it was 10/40 -- but it was given to me by the guy that bought it , but had no label that I could read (torn off) ... so it might NOT be 10/40 after all ..?

All suggestions welcome !
Thanks in advance,

Well problem solved new starter solenoid and 1st press and she started fine