The circled areas are not the relevant points for this issue. This is where the whole head assembly mech slides on. I can't really recognize where that arm is located, it seems to me it is below the white erase head (721AC FO5J6) on the left. Do not disasseble anything on the head assembly - this would deajust the head alingment.
If you move the white finger that is responsible for the auto stop system, you see what is moving. This is the part you have to make move freely. I don't know the grease you've mentioned, but I would recommend any silicone grease or that mentioned white grease for plastic gears. So because your grease is silcone grease, I think it's OK for this purpose. If everything is metal where the grease goes on, the type of grease is not so critical. But if plastic parts are involved (e.g. bearings!), be careful. Using the wrong grease may plastic parts make to break or to become sticky when time goes by.
Very important: Make sure no part of the tape way is contaminated with grease. After doing your work, clean the heads and every part that is in contact to the tape (erase head, auto stop finger, record/play head, capstan, rubber wheel) using alcohol to make sure everything is free of grease.