Why is my furnace pressure fluctuating during cycles?

Some needle movement when the valve opens and closes is normal, since the regulator inside the valve reacts every time gas flow starts or stops. What you're describing sounds like more than that though. A few things to check before you buy anything. First, what are you actually measuring? On a natural gas furnace the manifold pressure with the burners running should be around 3.5 inches of water column, or whatever the rating plate on the unit says. If you're seeing a steady 10 inches at the manifold, that's way too high and the furnace is overfiring. An overfired furnace will run rough and trip the limit switch from overheating, which gives you exactly the short cycling you're describing. If you're measuring on the inlet side of the valve, 10 inches can be fine, since supply pressure runs higher than manifold pressure. The bouncing during shutdown and restart could just be the regulator hunting, but on an old unit it often means the diaphragm in the valve is getting tired. I had a similar situation with an older furnace where the pressure would swing every time it cycled, and the valve was the problem. Replaced it and the cycling issue mostly went away.

Check the rating plate for the correct manifold pressure, then test again right at the outlet tap with the burners lit. If it's high, some valves have an adjustable regulator under a cap on top, and you can turn it down slowly while watching the manometer. If the reading wanders around even while the burners are running steady, that points to the valve or possibly the regulator at the gas meter, which is the gas company's side and they'll ussually check it for free. And obviously you're working around live gas here, so if you end up adjusting or replacing the valve and you're not fully confident with leak testing the connections afterward, that's the point where a pro visit makes sense.

That bit about the tired diaphragm matches what I went through two winters back. My furnace would lock out and need a reset every few days, and it got worse over a season or two before the valve gave up completley. One thing I'd add: take a photo of the valve label before ordering a replacement, because there are a bunch of similar looking ones and mine needed a specific model to match the wiring and gas type. Made the swap pretty painless once the right part showed up.

I had a similar valve failure on an older model, and before it completely locked out, the furnace started making this realy wierd whistling sound right when it was trying to start up. It wasn't loud, but it sounded strained, like the gas was struggling to flow properly through the pilot assembly. That convinced me it was the valve acting up before the pressure fluctuations even got bad. It saved me from worrying about a pressure drop on paper because the physical symptom was allready there. You shold listen closely when it tries to ignite before you start measuring anything.

Back in the day with the old standing pilot units, a sticky valve woud sometimes get another season or two out of a good cleaning or just reseating the diaphragm, but that's a gamble I stopped taking after one quit on me during a January cold snap. Had to run space heaters for three days while I waited on a part. If yours has been locking out for years like you say, I'd just swap it before it picks the worst possable week to quit for good.

Doing the swap yourself is very doable if the valve isn't buried. Mine sat right against the burner manifold and I wasted an hour fighting it with regular wrenches before I grabbed a set of stubby ones. Made the job take ten minutes instead of an afternoon. Also loosen the union on the pipe side first rather than twisting the fittings on the valve body, learned that the hard way. Since yours has been acting up for years already, getting the part ordered now while it still lights at all seems like the right call.

Update: so I paid closer attention during startup yesterday and there's actually a faint whistling sound right as it tries to light, which one of you described almost exactly. Sounds like the tired diaphragm theory fits my furnace too. I snapped a photo of the valve label like suggested and found the replacement part online for pretty cheap. Since mine already locks out every week or so, I'd rather swap it than gamble on cleaning. Is this a realistic DIY job or should I just book someone?