Hi beams and back up lights not working

2003 Chevy Avalanche 2500- Hi beams faded and went out at same time while driving. Lo beams work fine. Both fuses and relay are good (swapped out and checked voltage). You can hear a clicking in the relay when you switch between hi and lo beam.
Also, noticed both backup lights are out. Not sure when that happened or if in any way related to the headlights...
Is there anything else I can check? Thank you! (Head lights are my priority as I live out in the country)

DO you get power at bulb connectors?

I didn't check, as they looked awkward to get at...I'll have to have a look.

Reason I ask my son had similar issue and tghen lost Low beams.

Turned out the connectors became brittle over time and connection with bulb was lost... as plastic broke away..

Replaced the connectors and all is well.