This battery is essentially flat and well on the way to a very premature demise, so you are right, you need a "bit" more.
Best would be to replace the existing panel with at least a 80W panel and fit a reasonable solar regulator as well. Add a Trik-l-start unit or similar and it should keep both lots of batteries topped up while in storage. (mine is stored at Lancaster and my system works well)
Caution is needed if you just add a larger panel in parallel to the existing 4 watt one because often those systems don't have a regulator controlling the charge cycle because the small panel output current and maybe reduced maximum voltage doesn't require one.
If you go the way of feeding into the lighter socket, first check which battery is supplying it and whether it is live at all times. If you have to switch the power isolator on to have the socket live, then it is probable that all the phantom loads running will flatten the battery despite the increased solar input. Due to the very small amount of current supplied, especially during adverse conditions, anything as small as 1.5W isn't going to help much.
Looking down the aisle at night reminds me of landing at an airport - seemingly dozens of indicator lights shining - all of which add very little load, but collectively add up to an amp or more of 24/7 power drain