With my compl. reconditioned GL1000 K1 I had the same problem each time with the 1st starting in the new season after 6-7 months lay-off or after the storage of a couple of months.
Each time the electric starter had to turn quite a while before all 4 carbs were filled by the fuel pump and the engine was starting ......often accompanied with a sottished situation........and showing the first signs of life.........typically the behaviour of Classic Goldwings as far as I know.......
I now have a simple solution wich works quite well.........after max. approx. 3 attempts my engine fires up.
In the 2 pictures below (pls ignore the cans in both pictures) you can see the small plastic tube with a rattlecan adapter fitted on one end and a brass multi opening spray-nozzle on the other end.
This tube set which is used to spray tectyl etc. in the hollow chassis areas of a car is mounted on my bike in such a way that the spraynozzle is fed through the air infeed of the airfilter into the outer airfilter area ("box") of this.
Here I fastened it in some simple way.
The rattlecan adapter which has the proper size to also adapt the opening of a brake cleaner rattlecan or a start-help pressurized can is pushed under the upper tank lid of the faux tank.........the small plastic tube somewhere simply fixed in the region of the spring mechanism of the upper faux tank lid.
When I want to start my bike I connect a brake cleaner rattlecan to the rattlecan adapter and give my bike a shot of brakecleaner for approx 4 seconds.
As soon as i use the electric engine starter with the choke pulled, the brake cleaner which is highly flamable expands in the airfilter area rapidly and is picked up by the engine and ignited by the spark plugs........
The injected brake cleaner amount will let the engine fire and turn for about 3 seconds at a much higher rev. than the starter can.
It could be that you have to make another 1-2 attemps but than the engine starts running constantly.
It saves hard work for your starter and battery..........and your mood.
In fact, spraying some engine starting fluid in the airfilter box with a normal rattlecan would also work but the problem is that you can not reach the opening of the airfilter box.
Now you have a solution with a permanent located and fastened plastic tube plus 2 endparts........you only have to open the tank lid and connect the brake cleaner rattlecan.
Life suddenly is much easier as before.............I can strongly recommend this........also for "healthy" GL's, like mine.............
Of course it is assumed that all relevant accompanying parts and conditions are ok.