Single handed sailing and running backstays

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How do you tell if they are needed to hold the mast up, or not?
My running backstays are rigged in a weird and baffling way which chafes the topping lifts, and I would like to avoid using the runners if not needed. My boat is unique in Europe. Nobody knows.

The more "swept back" the shrouds are, the more likely it is that the runners are for tuning rather than essential support. On my boat, I was told that I could gybe the boat with the masthead kite up in 18 knots of breeze - without runners - and the stick would stay up. There was no permanent backstay, just the runners. I never tried it.

Your boat is gaff rigged, and is so far away from my experience that I can offer no opinion as to whether your runners are essential or not, but look for aft-swept shrouds and spreaders if you have them. And ask owners of similarly rigged boats. Even if yours is a unique boat, it would not be surprising to find others that are rigged in a similar way.