When adding a player to the 40, some have said: "His option clock starts sooner and he will go to arbitration sooner."

Is this true?

I thought service time was the only determining factor of arb eligibility.

And what does "option clock" even mean? Will he somehow lose an option? If so at what rate? 1 per season or what?

Players have 3 options.   Being on the 40 burns an option every year.

Has nothing to do with arbitration.    That's based on BL service time.

Arbitration is only determined by major league service time.  So adding a minor league player to the 40 has zero impact on arb eligibility.

The "option clock": a player has three minor league options seasons, in which he can be promoted/demoted between the minors and majors at will.  Any season in which he spends more than 20 consecutive days in the minor leagues will use up one of his three option seasons .  Once a player uses up all his option seasons, he will have to be exposed to (and clear) waivers in order to be demoted back to the minors.