Just to close the loop. The problem was the headlight switch. The plastic module had cracked and come apart. I replaced the switch and the interior dimmer switch next to it which had become lose from broken retaining clips and the lights work perfectly. Probably a result of the AZ heat. In the process I had noticed the headlight wiring harness had decayed with much of the wire coating cracked and missing. The wiring harness on the 2003-2004 C70 is not replaceable. So, Swedish Auto Werks in Phoenix rewired the assemblies for me and as a result they work perfectly. Thank you! One interesting challenge I encountered. I had opened one of the headlight assemblies to see if I could access the wiring. In the process I used "Invisible Glass" glass cleaner, which I use on all my cars tinted windows, and must have used too much or left on the lens too long. The product clouded and damaged the inner surface of the lens substantially. After extensive polishing with rubbing compound I was successful at returning the luster of the lens. All is well!
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Steven 04 C70 HPT

"...is the section of wiring that connects to the base of the bulb replaceable?"

After checking bulbs and fuses (look on the underside of fuse box lid for headlamp fuse numbers), the H7 bulb socket and bare / exposed wiring would be suspect.

ipdusa offers a H7 bulb socket with pigtail that can be spliced into the harness wiring where the insulation deterioration stops. ipd part number 120485.

If a more thorough repair is necessary, an entire new headlamp wiring harness may be required. Volvo part number 9438738.

Fuses will blow if bare wire on headlamp leads is making contact.

Address these items first, before suspecting relays or switches.