The brake switch runs the stop lights. It’s an input to the SBEC for lockup and cruise control..

While in cruise the assumption is that once the brake switch gets used that you want to stop, so shut off lockup.
You are slowing down so you want lockup disabled to prevent surging/bucking/etc.

Most engine driveability issues are exacerbated by driving in a higher numerical gear or in lockup or in manual transmission apps with clutch engaged.
Lower torque multiplication in high versus low.


Temperature having the effect on your truck sounds like to need to look at that very closely. I’m not a driveability guy but cold temp should make the truck rich - what if any effect on the miss I don’t know. But 60-65 degrees engine temp or higher and you get OD, lower you don’t.