Elizabeth, why not plan on re-invigorating the plant...as it is...in the whole instead of taking cuttings.
Not that taking cuttings isn't a bad idea...if you wish to use this as a mother plant and make lots more little plants, then go ahead...do that.
But, if its just a wish to have this plant come back to life for another season, then why not do that.

Here its almost time....you can stretch it if you like...do it now....or wait another week...two weeks....and
bring to a newspaper covered table....remove it from the pot, cut it back by 1/3....1/2......to about 4 - 5 inches.
Tear the roots apart, remove all the old soil from the roots.....and after removing all the old leaves, the stems, the broken or damaged, pot it up into fresh potting soil after putting some shards on the bottom of the pot to allow for good drainage, water it well and take to the sunniest window you have. (but don't use a north exposure..its not good enough)
Clay pot is an ideal one to use for geraniums.

Having watered it well to drainage, don't water again until new leaves begin to form...about 3 weeks or so.
Keep turning the plant 1/4 turn every day.
Don't feed until new leaves develop, then do so 1/4 rate 20/20/20....
Don't let the water sit in the saucer for more than 20 - 30 minutes...then dump.
In about 4 - 5 weeks, major leafing will develop....and maybe, before its time to put them outside for the season, flower budding will show.

Then switch over to 15/30/15...keep turning the plant 1/4 turn every day....or so.

Instead of making the plant try to perform under artificial light, why not consider just letting your plant sit the winter away in a cool, dark.....and dry location.