If you're spinning and gassing out, switch to mashing -- bigger gear, slower cadence.
If you're mashing and gassing out, try spinning.
You might find alternating between the two works for you. Works for me.
But keep in mind that outdated and cliched "spin to win" mantra was developed around refining the technique for young elite level pros during the EPO era. They knew spinning faster with slightly easier gears was more taxing to the aerobic system, but less strain on the muscles. The aero system recovers quicker, while tired muscles needed longer to recover (hence the adjunct use of steroids to help muscles recover overnight for the next day's stage).
But everyone tends to gas out quicker from spinning. EPO helped enhance the ability to spin longer. We mere mortals don't have that luxury.
And as we age we lose aerobic capacity quicker than muscle strength. Yeah, we lose both. But aerobic capacity fades quicker.
Over the past several years my cadence has slowed from averaging 90 rpm all around, 110 rpm on climbs, to 60-70 rpm all around. Occasionally I'll spin on short climbs, but more often now I get into a bigger gear and mash or stand to climb. At 65 that's about as good as it's gonna get for me. And a couple of years ago I started doing more walking, jogging, running and squats, etc., to strengthen my legs to compensate for losing aerobic capacity. Overall I'm a little slower on the same familiar 20-50 mile circuits I've ridden for years, but occasionally I'm as fast or faster on our many short, steep hillettes on our roller coaster terrain. I just regard those 30-90 second climbettes as sprints.
No idea whether my method would work on real climbs. We don't have any of that here. No mountains.