Some sort of restraint or chain

Wash-basin plug chain?

A search for "small cupboard stay" (perhaps mounted externally) or "sprung hinge" (use them to bias the cover open and have a latch to hold it down). Alternatively, arrange for the cover to slide sideways, or pivot it in one corner so that it swings out of the way and is held in place by a latch of some sort.

Replace the switches with ones with an appropriate IP rating and dispense with the cover.

How about a flat metal strut, one end fixed to the side of the control panel by a screw/bolt so that it swings upwards, had a bent section at the far end that holds the lid up. Maybe the bent section can be forked so that it fits either side of the plastic lid. Maybe the strut can be positioned so that when not in use it just tucks alongside the panel. All fairly easy to diy, otherwise buy a folding lid stay and adapt it.

I would use a helium balloon and a magnet. Ensuring the upper force was lower than the latched magnet.

There are some really small retractable mechanisms for keys and pens - I've seen ones you can wear on a finger, which hold a small pen. You might be able to mount the retractor below/inside the panel and run the wire through a small hole in the faceplate.

Is the lid when open near a wall to which you could fit a catch etc?

A picture might help as I at least can't fathom the options for what might be attached where.

Would a sink plug chain do it? They can be cut to length and come with fittings. You may need to buy two to get the fittings you want both ends.

I'm struggling to understand what a chain could be attached to stop the lid dropping shut. Don't you need some form of strut? Possibly an "over centre" one. Two bits, pivoted center and each end with a stop that only lets the centre pivot go little past straight in one direction.

Presumably the lid opens beyond 90deg.

Picture hanging chain as an alternative to bath/basin chain.

williamwright was thinking very hard :

If there is something above and at the rear of the panel, fix a bit of steel bar it lid or support, with a magnet to match it on the other part. You can buy good strong rare earth magnets, or pinch one from a very old, scrap 5.25 HDD. I use this method to retain my hut door wide open against the breeze, when taking stuff in and out.

What's really needed is a miniature strut. As you'd find on your tailgate.

basin plug chain?

Well plastic chains used to be used as restraints on lids. Its a pity Sony did not fit one on those little hinged doors on their VCRS. Brian

Ah, possibly but then the lids is not acting as an operational (partial) rain cover.

Can you get gas struts that don't want to be extended all the time or weak enough to just counter balance the few grammes of a perspex lid?