If I'm not mistaken, there is only one way for the newer version to go in because of the shape of the stick itself being more rectangular in shape (the part that senses the temp/level), so you put it in the same way it comes out, then line up the readout horizontally...it's only a quarter turn. We're all talking about three different part numbers here...
My instructions cover P/Ns 62936-00B, 62937-00D, 62938-00D, and 62939-00B covering 93-98 Touring models, 99 and later Touring models, 99-05 Dyna, and 92-98 Dynas respectively. I have the 62937-00D. The instructions as written indicate "Orient the dipstick so that the display window is horizontal and readable from left to right, with the Bar and Shield logo to the left (toward the rear of the vehicle). Push the dipstick straight into the filler neck until it seats against the flat rubber seal." As for removal "Carefully twist
counter-clockwise while pulling up to remove the dipstick from the filler neck. The dipstick should remove easily." The removal instructions are preceeded by a note which indicates "
It is important to twist the dipstick in a COUNTER-CLOCKWISE direction WHILE PULLING UP to remove. Twisting in a clockwise direction or not twisting could result in damage to the dipstick."
So, after looking at my instructions, I'm lead to understand that this particular dipstick bearing the P/N 62937-00D fits all FL Touring motorcycles built from 1999 until 2006.
After looking at the exploded view on the reverse of my instructions, it appears I have a model which screws together with three cross-tip screws on the underside of the display body.