Kurt I have always had the vehicle running to protect the alternator, as it's energized producing current at the time of the heavy amperage draw, thereby helping to keep both your battery and charging system up.
Go figure, another topic of difference, now an electrical engineer will correct one or both of us
V/R W Winget
Step e below:
One example from TM 9-2320-280-10 (Just a the first crap I googled not saying It's right or wrong...
2-23. SLAVE STARTING OPERATION
a. Position slaving vehicle and disabled vehicle close enough for cable hookup.
b. Stop slaving vehicle engine.
NOTE Vehicles with kits 5705623 and 5705624 and serial numbers 100,000 and above are equipped with screw-on covers.
c. Remove cover from slave receptacle of disabled vehicle and slaving vehicle.
WARNING Ensure all battery cables in disabled vehicle are properly connected before connecting slave cable. Damage to batteries,cables, or serious injury to personnel may result from improperly connected batteries.
CAUTION Use a twisting motion when installing slave cable to the receptacle.Forcefully pushing the cable onto the receptacle may cause damage to the receptacle mount.NOTE Ensure all electrical switches in both vehicles are turned off.
d. Connect slave cable to the slave receptacle of both vehicles.
e. Start slaving vehicle engine.
f. Start disabled vehicle engine.
Use a twisting motion when disconnecting slave cable from the
receptacle. Forcefully pulling the cable from the receptacle may cause damage to the receptacle mount.
g. After engine starts, disconnect slave cable from both vehicles.
NOTE• Screw-on type covers must be fully tightened to ensure a proper seal.
• For ease of removal, apply hand cleaner (Appendix D, Item 11)on the inside of the cover before installing receptacle covers.
h. Install receptacle covers on both vehicles.
i. Clean and stow slave cable.