Matt -
The line steadily lit is, as you guessed, probably a short on line 4s A/A1 pair. Troubleshoot this by lifting A leads one at a time till the lamp goes out. That set is causing your problem. Then find out why. Swap that set out with a known good set to see if it's a cable problem or a set problem.
If the lamps are bright on most phones and dim on one set, that set probably has the L & LG leads reversed. Check to see if it's a xconnect, cable or station problem.
Sam
