Is it safe to leave a Deltran Battery Tender Plus on a disconnected car battery for six months?

At the start of November, I completely remove the battery from the car, and attach it to the Deltran Battery Tender Plus. I leave it that way to the start of May. The car goes into storage for the winter, I take it out so it will not freeze and go flat.

I noticed that this year (and a little bit last year) there's a brown colored liquid leaking from it (I can tell it is brown since it is on a white table). It is a very tiny amount, but it will accumulate over time (after a month and a half the brown stain will be about 3 inches in diameter). I think it is coming from the top, I'm just wondering if this is the result of leaving the battery tender connected. It is still doing it a bit even when disconnected. The battery tender brings it to a floating amount of about 13.2 volts. When disconnected for a few days it stays around 12.8 volts.

Also just a side note, the battery was bought new in May of 2016. It is a Car Quest brand battery. The previous battery was a genuine Ford and lasted 12 years. I went with Car Quest battery not to save money, because the Ford one is hard to come by being an older car (they take a month to come in). My dealership currently has one Ford one in stock and I'm debating on buying it despite the fact I will not be using it until May.

Yup, that's fine. A float charger will not harm the battery at all. Set the battery up off the concrete floor on some wood scraps or at least on some cardboard to insulate it from damp cement slab ionic discharge or just leave it in the vehicle. A discharged battery will freeze as the acid is the antifreeze and becomes a lower freeze point when it loses it's ions into the plates at discharge.

Oozing means it's replacement time, I have 3 AC-Delco (2006, 2008, 2010) OEM's that still work in MN.
If you're in the market for a new one, I would go with an Interstate brand or the 72 month OEM battery.
Those discount brands use unpure recycled lead, so they don't last anywhere near MILSPEC standards.

Any Battery that lasts 12 Years is an absolute Winner. Your Battery Tender should not leak anything plugged in for a year. Replace it. It shouldn't generate enough heat to melt anything inside. But apparently that one did.

A trickle charger should not boil any water off of your battery if the battery was full of electrolyte to start with you can probably leave the battery tender on there for a year and it will keep it at peak charge without causing any of the liquid to boil away.

That's what a battery tender is for. Make sure the battery electrolyte level is kept up with distilled water. Tap water will ruin the battery.

It is better NOT to buy the battery. You buy the battery and use it immediately.

That's what battery tenders are made for.

Probably just gassing. This is why you have to check the water level while they're on a battery tender and top it off with distilled water.