Where can I find something similar to a fluorescent tube, with only one end for electrical contact
I would use LED replacement bulbs for Fluorescent tubes. With LED tubes there are some that are designed to work without removing the ballast and some that need to have the ballast removed. 

The ones that need the ballast removed and also require changing the sockets are the ones you want. Standard fluorescent tube fixtures come with shunted sockets where both pins are connected. Non-shunted means each pin can be wired separately. The LED tubes I've used that required ballast removal and changing the socket have come with non-shunted sockets but you can also purchase them separately. 

You can build a base and mount the sockets in it and have some sort of friction device to hold the tubes. There are obvious concerns about safety with having electric wires outdoors in a diy fixture but I'll leave that to other more qualified members to address.

I have some diagrams and pictures on how to rewire a shoplight for LED tubes which you may find useful.

The only issue is that all the LED tubes I've seen only have light coming out on one side. Not sure if that fits in to your plans but I think it's safer than having fragile glass in such a vulnerable location.