70bigblockdodge
Old Man with a Hat
My 2 cents, the clicking is probably always there but not heard because starter turns over drowning it out, most likely a relay to kill power to hvac system/blower motor allowing all the battery to go to starter. I would take BJS advice and ground starter relay direct as your nss might be not grounding when hot or infiltrated with trans fluid, do the reverse lights work all the time every time? this is the next thing I would go after, good luck.