Motor is wheezing, as if it's breathing - why?

It's a Honda lawnmower I'm asking about, which is about 10 years old, but
which runs fine most of the time.

I replaced the plug, ran a tank of fresh gas, and cleaned the filter, and
yet, it "wheezes" like it's breathing, normal rpm, and then slower rpm and
then normal rpm and then slower rpm and then normal rpm and then slower
rpm, etc, ad infinitum.

The interval is only about a second or two at most for this
stoichiometric:lean stoichiometric:lean stoichiometric:lean cadence to
occur and the stoichiometric:leancycles are quite regular.

The (California) carb on this thing is not adjustable (AFAIK), and the
choke shuts off in seconds as it's merely a slider that glides back in
place in a couple of seconds after initial activation.

Even after a half hour of running, the stoichiometric:lean wheezing only
gets slightly less pronounced, where the stoichiometric:lean wheezing I'm
talking about is when there is no load (e.g., it's sitting level on a
sidewalk). (Under load, it's harder to tell, but there's no "speed"
adjustment given I have the throttle bar on the handle taped tight in the
always-full-on position.)

I'm thinking it's all in the carb - i.e., choke and/or throttle...

So I guess it "could" be the throttle bar vibrating, but I don't see how;
and I guess it could be the throttle cables vibrating I guess, but again,
what can I do about that?

What could be causing this cyclic RPM change?