Quick follow-up: I removed the resin table for access. Removed the retainer clip, pulled out the end and looked, and the venturi was caked over with crud. I scrubbed it off with a small wire brush, confirmed the orifice was clear, and blew out the tube with compressed air. Put it all back together, installed an LP bottle (the protective yellow cap was still in place on the fitting, confirming the previous owner had never used it), and it lit off on the first push of the igniter. I’m very happy.
Unrelated, but thought I’d mention it: I was hoping to restore the black color of the plastic lid handle, and I thought I’d try an automotive product I had on my shelf called Back To Black, meant for car bumpers and trim. It didn’t help it at all.
Thanks for the help, it’s very much appreciated.