Recently there was a question here regarding exactly this cheap LCD, pointing to the correct data sheet & tutorial, but misinterpreting the pinout of the IDC connector (wrongly wiring the poti to pin 4 instead of pin 3).
The pinout in the datasheet doesn't show the connector side, but its solder side, the odd numbers being next to the display bottom up. So I've tried and the LCD worked as expected:
Sorry, actually my input should have been a clarifying answer to an assumption some month ago, where the photos still show a wrong wiring. Some of the rare google results for this particular model point to that misleading contribution. Additionally the module doesn't show any of the usual hints regarding pin 1 and even in the data sheet it's hard to find the weak sketch of the pinout.
In my photo the AV1623 is not upside down and it's aligned with the pinout sketch. The blue LCD is just added for behaviour comparison, not for any pinout considerations.
Maybe this information might be helpful to other users, which didn't receive a correct answer from google and were not sure if the AV1623 is really working as well as the ones with the "common" pinout.
Look at the photo in #2 of your link.
It shows a box male header with pin #1 at top-left. There is no ambiguity with a keyed header like this.
However, I would still follow the copper traces to verify that pin#1 is GND.
A square pad, a white dot, a keyed header, ... are all good clues when it comes to identifying pin #1.
All the same, mistakes are sometimes made with pcb layout.
You're right, there should be no ambiguity with a keyed header and there should be a visible hint on the PCB. But you can forget about this module's header key.
As outlined before the odd numbers are the ones next to the display. This deviation from standards might be useful to know for AV1623 owners, who don't want to consider datasheet mistiness or copper tracing.
At least it should solve the original questioner's problem.