Brake light switch replacement -- what's the trick?

Hi all Haven't been here in a while and it is good to see the same people are still here.
My 95 Integra automatic yesterday started to have a problem with one
not being able to get the transmission out of park, even with the brake pedal pressed. When I looked at it closely, I also found the brake lights out. The horn still works (same breaker). So after some fiddling around, got the old switch out and tried a new switch by just plugging it on to the connector - brake lights work again and the transmission wants to get out of park again.
My problem is: how does one get that connector back in? There must be a trick to it. I can thread the switch back into the pedal mount but the connector just does not want to go back in. It seems like the wire to it is exactly long enough that it is ok once it is in but there's not enough 'give' to bring it back up. There's also sheet metal and a wire loom in the way. Of course, this is not the most comfortable position to work in..
So what's the trick, if there's one? Does the whole pedal assembly have to come out or something? I'm right now debating to just extend the wires to that connector by soldering some new ones in between but hate to mess with factory wiring.
TIA Remco

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