cig lighter relay?

This is probably an odd question, but I am curious if it is at all possible to have a switch to change my cig lighter from constant power to accy power. It is currently in its factory configuration to turn off with the car, but on occasion I would like to be able to turn it on constant power so I can charge my phone with the car off. I am paranoid about parasitic draw so I don't want to just change the wiring to constant power.

No problem just run a direct feed from the wire feeding your fusebox from the battery and fuse it at 15 amps.
No relay needed.
The only parasitic draw will be on leaving the charger in the lighter.

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Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.

Although Howard omits the switch so therefore the cig socket is always powered (constant +12V), there is no parasitic draw from the socket itself - it's only if you have things plugged in and on.

I have always had constant +12V cig sockets (and radios & HUs etc). Even when I have mistakenly left things on - like GPS etc thru the cig socket (or left the HU on either paused or no volume) - I have had no problems for a day or few.
Mere charging of phones or GPS etc should be no problem. They are a relatively low load anyhow, and that decreases as the battery charges.

Besides, an actuated relay to connect constant +12V would itself be a 60-250mA draw.

I omitted the switch because the OP said "constant" else it could have been left in its original state.
I wonder if our OP understands no need for a relay as much as he or she misunderstands the meaning of parasitic draw.

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Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.

Fair enough. I was referring to his first line re having a switch to select between the two (ACC {else IGN} & constant.
Alas a switch - or relay - involves cutting into the existing cig socket supply - else duplicating it - and since IMO it is fine having a cig socket to constants +12V (rad: often that's desirable).   
In short - no switch - just rewire to constant +12V (ie, battery +12V via a fuse) just as you suggested.


As to parasitic draw, I often read where people think there (might be) a parasitic draw with cig sockets. I have no idea where they get that idea from, after all even a lighter is not drawing current until it is pushed in - but it is a common theme in webland.
Maybe such people use those health damaging air fresheners....? [ Or cig-socket battery chargers to keep their batteries fully charged? (ha fracken ha!) ]