If you have the means and are serious about improving then I highly recommend buying a power meter. I have Favero Assioma pedals which are about the cheapest option for dual sided power and work well. After I've been riding for a while I tend to slack off and fool myself into thinking that I'm working harder than I really am. The power meter keeps me honest.

But without a power meter you can certainly pace yourself by heart rate. Figure out your heart rate zones and then do some test rides holding your heart rate steady in a particular zone and sustain the effort as long as you can. Then you can estimate a maximum target heart rate for each climb segment based on how much time it should take.

You can also experiment with different pedaling cadences. Every cyclist has a different optimal cadence, but in general you want to shift down when climbing and keep the cadence high (unless you're intentionally doing a low cadence strength workout).

Correct me if I'm wrong...

So if I have a power meter I have instant feedback on the power level, and if I know my target power level I can work up to it without overshooting.

HR, unlike power, is a lagging indicator so I am likely to overshoot, especially if I am poor at pacing to begin with.

Yep, HR can tell you a lot (power meters are pricey, but indeed are the best option). If your HR rises too quick you're likely off pace however though.

Another thing you can do is thinking of saving some gas in the tank for the last bit of the climb where you'll sprint as you summit. Start with this in mind at the bottom