Let's see if I can get this right. The solenoid has 2 windings. It has a pull-in and a holding coil. The pull-in is paralled to the starter contacts, . Closes on key start. Contacts in starter arc together, leaving pull-in coil energized, and possibly starter engaged. Hard to hear w/engine running. Smokes starter, plus solenoid, they say.
The holding coil is energized by key/run position. This gives you your manual overide of the linkage option.
Alledgedley starter contacts last only 100K miles. Could be less if you're using non-filtered electrons. I changed mine after that , they were okay. About $30 in parts for them. Easy job.
This is the most common scenario with that sympton.
Relays and solenoids also have been known to fail.
Apparently Cummins has changed the design of the replacement solenoid, needs bracket mods and tweaking or somesuch.
E-bay is a good place to look for those n. i. b. old style solenoids.
There are a person or two on this board selling contact sets for the starter. There is also someone on e-bay sells full rebuild kits for the starter, w/contacts,bearings, and I think brushes, for not a whole bunch more.
Have fun
P. S. Oh yeah. It is a fuel cutoff solenoid, right at the end of the P-Pump. It shuts off the fuel supply to the pump, thus the engine, and vice versa.