12v multimeter readings from your battery don’t necessarily mean the battery is good.
The clicking sound is the starter relay trying to sap enough power to click over and feed the starter motor.
A known good fully charged battery is essential before you look anywhere else.
Symptoms are …Relay clicks like its got a dead battery and engine does not turn over … but you do not think its your battery but you do think an oil change might cure your issue!!! … Your like a dream customer to any mechanic
Clutching at straws that it’s not serious!! Look not being nasty but your faced with the possible simplest of issues here. Have you made any attempt to do anything other than clutch at straws in a mechanically inept manner? Charged your battery? Push started the Bike? 13 v means nothing it’s not volts that starts a bike it’s amps. And your oil light is on due to the oil pressure being very close to 0 when the engine is not running. Stop talking nonsense and go and do something then we can eliminate problems… Get your battery load tested and charged would be the best start to the job.
Clicking noise on my R1 always tells me I havnt ridden it in a while and there is not enough power in the Battery - bump start always works as does charging the Battery - that is your issue almost 100%!
Edit- just noticed this is in sports bikes… WTF! Lol