I know absolutely nothing about Independent watches, and I am not sure what the small oval knob at 2 o'clock could be. The knob might be a means of starting and stopping the movement, or it might be a means of setting the hands. I don't think it has anything to do with opening the case.
If there is no way to open the back of the case, then the movement must be accessed from the front. Open the front and see if there is a small lever or catch just under the dial at 6 o'clock. Lift this and the dial and works should hinge outwards revealing the movement. If it is a stem wind watch, it may be necessary to pull out the stem (as if you were setting the hands) before lifting out.
Worth a try. The only other option I can think of is if it a screw-type case, and there the back will open like unscrewing a jar lid. There won't be a groove for inserting thumb nail, but you should be able to see a fine line.
Hope this helps.