I was able to separate the screen from the board.  It took several attempts and in each attempt, I tore the cable ribbon each time due to some glue that was use to secure it. So i decided to leave it attached to the board for now.  There was number on the ribbon that was the only indication of a part number.  It lead me to an alibaba page  (https://www.alibaba.com/product-detail/0-96-tft-lcd-display-80_62563989971.html) and I was able to use that information to search for more information.

After much searching, I found a pinout that may match the ribbon cable.  Locations of the ground plane as well as a K and A marked on the back of the ribbon, which I assumed was for the backlight anode and cathode, gave me an indication that I had the proper pinout for the screen.  

Now I have a pretty decent idea of what I'm working with.  Its a .96" 80x160 pixel display driven by a ST7735.  It operates on 3.3v and there is 13 pins on the ribbon connection. However, theres 11 connections (far left side in image below).  I ran a power supply, voltmeter and continuity tester to identify as best as I could which of the far left connections, connects to the ribbon connector.

Finally I took a fresh screen and soldered wires onto the old header pins.  With this I should be able to talk to the display.  Next I'll decide what microcontroller or arduino to use and methods to test.  While i was doing this, I did find out the vape had a arm controller(32 bit arm cortex +m0cpu) as well as a small possible flash, probably for image data.  I didnt dig more into this but I plan to in the future, possibly as another project.