The plunger thingie on the end doesn't do squat for that center pin. I looked at the picture of yours and it APPEARS your pressure differential valve is somewhat centered. Can't say for sure, but it looks like it. There's a divot area that should line up under that hole. The tool may not be able to seat fully. It doesn't have to as long as the d/p valve is centered and the pin goes all the way down to touch the center skinny section. The idea is the pin just keeps the d/p valve from moving when bleeding them. If it moves off center, you're f***d. There's only one way to re-center that and that's take the valve apart, which is a PITA. Might as well rebuild it while you're in there and put new seals in it. I've done it and it's not for the faint of heart. Well, there's another way, and that's crossing fingers and doing a hard and fast stomp on the brakes and hopefully the d/p valve will reset. Doesn't always work though. If it does, you can usually "feel" a discernable pop.
Look carefully at yours inside the light switch hole again and see if the valve inside looks like it's centered like it is in the picture below. If it is, screw the tool down until it stops, then bleed dem brakes!