I'm pretty sure this is indicative of a BCM but it's intermittent and always happens when I am away from my tools. Ignore my rambling I'm weird as hell.
Check your grounds, and your battery cables. A family member had one of these (ZJ) that was doing something similar. It ended up being the battery cable ends kept loosening on the battery and were making a poor connection. I replaced the cable ends and the issue stopped.
On these sometimes the battery cable clamps crack and cause low voltage, I replaced both of mine on our ‘98 Grand. What I did was cut off the old clamps, crimp on cable terminals with a heavy duty crimping tool and bolt on marine grade battery clamps. These separate clamps can be easily replaced when they get corroded.
Other causes:
Bad grounds
Bad ignition switch
Head over to www.jeepforum.com and post this question on the ZJ Grand Cherokee forum I’m sure someone will have an answer.