That part looks like a relay for the grid heater on my 6BTA 5.9. Do the 8.3 engines use grid heaters for preheat and smoke reduction after starting?
If they do, and the relay fails, the preheat system won't work. Expect slower starts with more smoke. On my engine (6BTA 5.9, 330 hp), Cummins recommends a starting aid (i.e. preheat) any time the temperature is below 50 degrees.
The problem with the preheat system is it draws an enormous amount of power, something like 100 amps, and by default it cycles whenever the engine is running below 950 or 1000 rpm and the intake temperature is below a certain temperature. I can't remember the temperature off the top of my head, but it's something pretty high, like 90 degrees. So when you're in a long no wake area, the preheaters keep cycling, putting a huge load on the alternator creating a lot of heat in the relays. Eventually the relays fail, so it's a good thing you have a spare!
I have a switch at the helm so I can turn the preheat system off entirely. I typically use the preheaters when I start the engine in the morning, especially in winter, but quickly turn it off to avoid the big electrical drain.