It sounds like you do intend to use it from time to time maybe? If we're not prying, WHY are you giving up on the hobby?
Lots of good advice here, depending on your detecting plans. My two cents...
Taking the battery out is overkill. It's not trivial on an Equinox and may affect the water-proofness. Plus you'll be re-installing it regularly to keep it charged about halfway? Plus even more annoying if you want to USE the detector from time-to-time.
Storage in a shed...not ideal but might be ok. The manual says this:
• Do not expose the detector to extreme temperature conditions.
The storage temperature range is from -20°C to +50°C (-4°F to
+122°F).
I'd rather it was in the house somewhere, but based on that, a shed might be ok. I WOULD put it in an AIRTIGHT bag -- with dessicant packs if you have any -- to keep humidity away from the detector, certainly in the shed, and couldn't hurt in the house. As someone said, under a bed, back of closet, under the stairs...pretty much ANYWHERE climate-controlled inside a house is better than "the shed."
Oh, from my standpoint, just a hobbiest, not a detecting god, metal detecting technology advances at a snail's pace. I consider the Equinox incrementally better than the Fisher F75, which was released in 2007. An Equinox will still be viable in 10 years. Keep it!
Hope this helps.