best i can tell from the wiring schematic those 2 relays you speak of K11 and K12 which are listed as K31 and K32 in the schematic are for the horn and travel alarm. The reason the K12 (K32) relay is not pulling in is because the settings in the programming are probably turned off so the relay is rendered inactive untill one of the travel alarm settings is set.

my best guess about this

now as for the contactor when the system is turned on it tells logic to supply negative to the K11 coil and to the horn circuit side of the relay.

as for the display it gets its positive power from the keyswitch circuit directly. Negative is fused with a 2A fuse.
Since your getting intermittant display power you may want to pull the display panel and check all the connectors, check the fuses in the fuse strip and make sure both circuits on the keyswitch are working properly, it is double pole switch.

The only other issue i can think of would be some issue with the logics.