Majority of newer battery maintainers (from Battery Tender Jr and C-Tek) auto sense if AGM or lead. Maybe try a new try one? Anecdotally I've had maintainers last 10-12 years but also had a BTJ one go bad in less than 12 months - ended up killing an AGM battery in short order but Costco took the BTJ on return and w some persuasion helped cover cost of replacement power plant.
Anywho, pop tow hook cover and see if previous owner relocated emergency release to that location (assume it's a 2000 Boxster based on your username). You can also delicately "fish" for it w a small wire/coat hanger under the passenger side headlight. It'll look like a twisted strand thicker piano wire and if you can locate it should be taped into place if still in OEM location.
If you want to start up to prevent drain, you can but just need to ensure gets up to full operating temp to help burn off moisture generated, etc... think minimum 15-20 minutes.
Also, for opening frunk... maybe have an assistant gently apply downward pressure (or upward as well w a plastic trim pry tool)) to frunk lid whilst you try releasing again. Otherwise, as JFP suggests let it sit and tackle when all warms up again and once you resolve, use a pigtail connection for maintainers directly to the battery... skip the cigarette lighter options.
Good luck
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