Disclaimer: The procedure I present in this post reflects my own experience. The description may be incomplete and might even contain errors. Consider that I am just a self-taught hobbyist, not a trained professional. Copy this procedure at your own risk! Also, consider that any attempt to disassemble and repair a camera carries a certain risk to worsen its condition or to even breaking it completely.
Remark: The described procedure may also work for other cameras where the back cover is opened by pulling up the rewind knob. However, I didn’t test this and you have to try for yourself.
It is always a good idea to remove the back cover (“film door”) of a Canon A-1 during repair, preferably before you remove its rewind knob and rewind shaft. However, we are all human and may forget this in the heat of the moment. If worse comes to worst, you might then close the back cover accidentally. @#$%&!
There is no “regular” way to reopen the back cover in this situation. Before I present my hack of how to reopen it anyway, we should have a look at the regular opening procedure.
The resting position of the rewind knob is flat on the ASA film speed dial. You pull up the rewind knob to its upper position, about 1cm above the dial. You will feel the rewind shaft snap into place. The back cover is still locked. Then, you pull up the rewind knob another 2mm (against spring force). The back cover gets unlocked and you can open it. Technically, the unlocking is initiated by two small lugs at the bottom of the rewind shaft that lift a small ring at the top of the film chamber, around the shaft. This ring is attached to the locking mechanism and will unlock the back cover then lifted by about 2mm.
With this knowledge, it is easy to find a hack to open the back cover without the rewind knob/shaft. All you need is a standard 1″ paper clip. You bend its outer loop straight and then bend a small hook to its end (not more than 3mm wide).
Then, you insert the hook end of the paper clip through the rewind shaft guide into the film chamber (about 15mm deep). Finally, you pull the paper clip upwards, trying to catch the unlocking ring with the hook. If you have managed that, pull up for another 2mm against spring pressure. The back cover will unlock and you can open it. Voilà!
Final remark: If you look down into the guide of the rewind shaft from above, you might see a small metal bar. This bar is not part of the locking mechanism of the back cover but is only a metal clip used in the latching mechanism of the rewind shaft. Therefore, there’s no point in pulling it.
That’s all.