an L4034 has 18 pins
an L2014 has 16 pins
On both displays, 2pins are indeed for the backlight.
You don't just hook-up power to these 2 pins. They need a pot on the ground wire.
Look at the different schematics, then you'll know what I mean:
About ordering from eio.
Well.. it certanly is not the best company around, and sometimes it takes some time before it gets delivered.
But I haven't heard of anyone who didn't get anything which he had ordered.
If you want to know more opinions about EIO use the search function. they have been discussed many times
Hope this helps you out !