Now that is unusual method of bulb contact. I wonder if this is fluorescent light or something else

Looks like an instant start F4T5??

Nice!, Interesting contacts on this lamp

If the outer shell is one of contacts, i would guess it is normal fluorescent, only with weird sockets (assume such socket s on both ends)

could be a Cold Cathode Lamp

Both ends are the same and it's the same size as a normal F4T5 lamp. I'd like to try lighting it but I don't want to damage it.

@Colin: As cold cathode it would need only one contact for each side, so not use the shell as contact, if there is the central one.

@DimBulb: Try to take the Ohm-meter and measure the resistance of the "filament". If it has about 10Ohms, it is signature for "standard F4T5".
Then i would try to connect the filament to 3V supply via an A-meter. If the current drop after few seconds down to about 0.1A, there definitely is filament, that match the F4T5.
In such case i would try to find F4T5 preheat ballast and light it. Measure the voltage across the lamp and in case it is about 25..30V, so in that case i would conclude, then it is F4T5.

Thanks Medved- Everything checked out so I tried it and posted a "lit" pic.