Every garmin gps is different- some run on one specific voltage others can handle a wide range. My 376C can take up to 24 volts. The 2720 is designed specifically for 12 v, with a max of 13.8. You kind find this info in the Appendix to the Owners Manual. The 2720 cig lighter has a 1 amp fuse inside it, so if you want to go direct to the SAE you best add a 1 amp fuse inline.
Do not cut the wire , do not monkey around with it, because you will lose the functionality of the cig lighter voice . The cheapest easiest way to get what you want is a cig lighter female to SAE plug.
https://www.ascycles.com/detail.aspx?ID=47968 . There are many many sources for this gizmo, or you can make your own .
Another easy way to get what you want is to take the 110 V wall plug and cut it in two and put an SAE connector on each cut end. Connect the two together to use in the wall socket and to use on the bike just use the end with the SAE and the garmin plug. If you cut this wire you will see only one power wire , the ground is a kind of foily wrap that wraps around the pos wire. You can easily connect this ground thingamajig to the neg wire of the SAE. I have done this with happy results for 2 years , no sparks no smoke. :yahoo: