Answer

In principle, opening a refrigerator door when there is a light inside that turns on is an unintentional act, but here it is a case of an inevitable result: the light will certainly go on, although perhaps one does not care about that if it is daytime. In Jewish law, the halakhic decisors rule that this too is forbidden. It is also hard to view this as indirect causation.
However, when you apply tape as you described, there is a chance that it will hold and the light will not go on, even if the odds are that it will. Therefore it is not considered an inevitable result, and we are left with an unintentional act, which is permitted. Note that an unintentional act is not a leniency based on duress; rather, there is simply no prohibition here. So even if there is a real concern, that does not change the status to forbidden. If, over time, you gain consistent experience showing that after a certain hour it no longer holds, then from that hour onward it will become an inevitable result (but not before then. A safety margin is relevant only when the leniency is based on duress. With an unintentional act, it is a genuine leniency, and a safety margin is unnecessary).
Therefore there is room to be lenient, but in my opinion it is preferable, at least from an educational standpoint, to remove the bulb entirely (for the Sabbath or altogether), or to find a more effective way to keep the switch taped down (maybe more tape. I remember that in the past people would hold the switch in place with a matchstick or toothpick for the entire Sabbath so that it would stay off).