Dave Harwood, Blue Flounder, #155
Everything I've read about multiple battery banks suggests that while it's OK to charge the banks in parallel, they should be used in parallel only when neither one is strong enough for the required task (such as starting the engine) and NEVER left in parallel ("both") for extended periods. The reason given is that (unless they are of the exact same type, were bought at the same time, placed in service at the same time and were ALWAYS used in parallel so that both received EXACTLY the same wear) one will be weaker (not able to hold as high a charge level) than the other and the stronger one will discharge into the weaker one. As the weaker one continues (for whatever reason) to lose charge, it drags the stronger one down. Much better to leave the bilge pump connected to whichever battery you feel is stronger.
There is also a piece of equipment available (I've seen them at West Marine) called a battery combiner which prevents parallel discharge but allows current to be drawn from both when the demand warrants it.
Leaving two batteries paralleled across a charger is OK, with the understanding that there will be some internal discharge during the night (and on cloudy days) when the solar source is inoperative. The diode that prevents night-time discharge of the battery into the solar charger is in the wrong place to prevent the weaker (paralleled) battery from draining the stronger one. I have to point out that the charge on the individual cells of a battery do NOT equalize, because the cells are connected in series. Parallel connection of two cells would again allow the weaker one to degrade the charge of the stronger one. When a 12v battery with six cells eventually fails, it is often because one cell refuses to hold a charge while the other five are still functional. If you have two 6v batteries connected in series to provide 12v service, you only have to replace half of the bank when one cell dies. (The new 6v should be of the same size/type as the surviving 6v to keep the charging system operating properly.) The huge batteries used on the early Pullman railroad cars featured independently packaged 2v cells, connected in series to supply the required higher voltage. This allowed the lowest possible maintenance cost - you never had to scrap a working cell because a sibling cell (packaged in the same case) had expired. There was an outfit (I think they were located in WA) advertising battery packages of this type in the boating press several years ago, but I haven't been able to find them now that I'm ready to put a large separate house bank on my boat. If anyone has a lead on that subject, I'd like to hear about it!