The other three burners ignite fine, but you have to replace the wiring harness which includes all 4 ignition switches. The only tool strictly needed was a T15 torx screwdriver to remove the 4 burner tops which hold the cooktop down on the counter.
It took 10 minutes from start to finish. Granted, this is the second time in 12 years I've had to replace this harness. When I was done, it looks like the underlying root problem was that the switch in question's plastic housing has a plastic tab the holds it shut on the wires and that tab had broke, so the housing was slightly open and not making contact with one of the wires. That shouldn't happen, that plastic tab shouldn't break, especially since there's no stress or movement against it. And $45 is painful for this simple harness, but what are you going to do. And $700-$1000 for a new cooktop makes $45 to do a simple repair look not so bad. Anyway, it's an easy repair anyone can do.
No tools are necessarily needed to remove the old or install the new harness itself, except... maybe a pair of needle nose pliers if you have trouble removing or installing the ground wire connector and maybe a tiny jewelry size slotted screwdriver to aid with taking apart the plastic slip connector of the other wire, and maybe some WD-40 for the torx screws if needed.
Works fine now.