Does it matter that a cable is being used to connect the two units?
Not especially but I have found that not all cables are equal. Something to bear in mind if your original cable gets damaged.
Do you do anything to protect the cable and spcket when it rains?
I charge (Wahoo) directly from my hubdynamo or sometimes a powerbank but until recently never in the rain. There usually is no need. Water will damage both my hub charger and GPS - that's too big a risk on tour. But it's rarely an issue.
Sometimes I get as little as five or so hours.
it can be a bit of a stuggle, especially on very overcast days when I might need to have the screen lit for much of the day's ride.
I think this really is your problem. Unless you have poor eyes you shouldn't really need the light on in those conditions.
Can you compare your unit to someone else's?
Have you reset/revalibrated battery meter?
Good advice
Why not set it to light up for 15 seconds on demand?
Excellent advice
A big part of your issue is conserving energy.
found one or two 30 min blasts were generally up to my requirements.
I think this is important
I have my Garmin Edge plugged permanently into a Power Bank
I've been of the belief that rechargeable batteries should be regularly let run down in order to preserve battery life.
In an ideal world I'll have a good approximation of how long I have left on my unit and recharge as necessary. If that happens to coincide with rain then the GPS and powerbank goes in my Barbag to be checked as necessary. No rain no problem.
As an aside, a simple, cheap solution is from
Decathlon. They have a foldable mini rucksack (string straps) that will go over a bar bag and unit and can be tied off. Waterproof, ugly and you'll still need to peek under it to see the screen but it doubles up as a very handy shopping bag. I paid €1.99 for mine having lost my original rain cover.