Proper Way to Insert Multi-Probe

Yep, agreed.
Store the probe so it stays clean (lot of times we use one of the ASx side cockpit vents, also helps keep peeps from dropping something on it.....), wipe it off a few times a year, very thin smear of lube, twist while installing.
Yes, the "witness mark" tape is nice. If for some reason the probe sorta "hangs" on install, you may have a huge system leak/cross talk if it's not fully seated. Yep, did a spring flight like that once, helped fine tune my butt vario...... Just twist it in until the tape is against the tube in the fin, align the angled probe as required (some say straight up, some say straight down....).