Does conquering Targon's Peak several times in a turn cause the player to ready 2 runes each time?

Ruling: No. You can only score at each battlefield one time per turn. If you've already scored there, you can't conquer it again that turn, which means conquer effects like Targon's Peak don't trigger.

Sequence:

• If you hold a battlefield at the start of your turn, you score it once
• Moving units away and back creates a showdown but no additional scoring occurs
• No scoring means no conquer, so no conquer effects trigger

Nuances:

• You CAN conquer a battlefield on your opponent's turn if you started that turn with control of it, since you haven't scored there yet that turn
• This would give you a point and trigger conquer effects, though Targon's Peak's effect wouldn't be particularly useful on an opponent's turn