Okay, great, I can help. Yes if the middle sensor fails will cause your concern, and removing wiring to install a kit, is possible to agitate a possible open in wiring as well.
Sensor will see excessive exhaust heat after the dpf and shut off truck as a safety measure. If the wiring itslef is open, will cause the same concern. Does the truck currently start? Has this happenend intermittently, on and off? Most importantly, is there a code saying egt 1-2 or 1-3 fault?
Hi, sorry if unhappy with answer, I can continue to help if wanted, will work with you until problem fixed, or atleast pointed in right direction. Main thing, is there a code, pointing to exhaust temp sensor, 2 or three?
is the programmer able to read codes? if so have you attempted to read any codes?
Next, if click is coming from dash, and not starter, batteries will not be at fault, you are correct, if coming from under dash, or a relay box, there is a electronic fault, or network fault here. If happenened as soon as update installed, most likely is related. A corrupted program can, cause the problems you are having, but can not be verified unless codes are scanned.