Copied all commands out of the manual of the HP5803B to try them (not all, skipped serial settings and firmware upgrade commands for obvious reasons). Found some more interesting commands:
DIAGnostic:LIFetime:COUNt? value returned represents 3 hours in the HP, that would be nearly 4 years for mine
GPS:INITial:DATE 2016,1,29
GPS:INITial:TIME 23,59,01
GPS:INITial:POSition N,1,1,1,E,1,1,1,0 (not sure yet what the difference is with GPS:POSition)
you can set date/time and/or position to speed up the survey. I'm planning to use it only here in the lab, so i probably poke the coordinates of my house at startup
Other stuff:
GPS:POSition:SURVey:PROGress? +0
SYNChronization:HOLDover:DURation? +0.00000E+00,0
SYNChronization:HOLDover:DURation:THReshold 123
SYNChronization:HOLDover:DURation:THReshold? +123
SYNChronization:HOLDover:INITiate "Data corrupt or stale"
SYNChronization:IMMediate "Execution error"
*CLS
SYSTem:LANGuage? "INSTALL"
DIAGnostic:QUERy:RESPonse? +123