Electrifying it might not be such a big task, and might not be necessary. Since the entire stretch is outdoors, a diesel line could run from Grove Street to, say, Arlington Station (abandoned station between Elm and Forest streets in Kearny). A second track wouldn't necessarily need to be run the full length immediately - perhaps, a special side loop (forgive my poor vocabulary with regard to these things - I know there's a name for it but I just don't know what it is) could be installed at certain points to allow trains to go around one another, or it could just be a straight shot - light rail trains are all designed to be double-headed for just such a situation.
Personally, I like the idea of a diesel line (or whatever new fuel NJ Transit wants to try) on a straight shot like that. Start at Grove Street, hit Silver Lake, cross Franklin Street and transfer to the extension, create at least two or three stations between Franklin Avenue and McCarter Highway (before it merges with 21). Good areas for consideration would be Mount Prospect Avenue and Washington Avenue. Mt. Prospect can be converted to a station with almost no effort - throw some concrete on and you've got a nice, open-air station. Washington Avenue (or Broadway as it's technicially known in Newark - this site is the newark/belleville border) needs a stairway and some concrete and it'll be ready to go.
The area at McCarter Highway is somewhat dilapadated, but it could easily be converted to parking lots for commuters (and it's a prime position - I'm not sure how familiar you are with NJ roads, but 21 is a major artery stretching from Elizabeth to Hawthorne and intersecting with most of the major highways in northern NJ). Crossing over the river, the bridge would probably need some repair work but frankly if the line formerly handled major trains back and forth, light rail trains would be more than supported all the way across.
On the other side, there's room for at least one, perhaps two stations before getting to Arlington. The first place would be at South Midland, where the bridge meets Kearny and the light rail would be making landfall. Another place would be Belgrove Drive, which actually has a very nice road block in place separating it from the tracks and preventing traffic from crossing the road. Still another place that would be a good spot would be right before the train would cross Kearny Avenue - I would imagine stairs going from the bridge down to the rails would make a great station (a similar setup is used at Kingsland Station on the Main Line out of Hoboken).
And then there's Arlington Station. Right now there's a parking lot from when it was a fully operational station (assuming it was NJ Transit station), which makes it perfect to take over as a major stop for this new extension. Past Arlington, the line goes through an apartment village before crossing into open land and making its way to a permanently-opened bridge under the Turnpike and going to Secaucus Junction.
Honestly, for a start it could just be the line to McCarter Highway, then another phase to Arlington Station, then the final phase out to Secaucus.
*deep breath* OK so what do you think? I'm debating contacting NJ Transit with this, but I'm not sure how to do it and who to talk to. I'm also not sure if I need to pay them something to bring this idea to them.