My experience with led lighting has been good, while at the same time my experience with the switches or controls of led that come in them or attached to them is usually bad.
I don't know what kind of "strip lights" you have, but they typically are controlled by...
A thermal sensitive switch that senses the warmth of your finger.
An electrostatic switch that builds up a very small charge and you are the ground when you touch it.
A radio frequency (or worse,,,, an infrared band) is generated by a remote and the receiver is triggered by using the remote.
Or maybe a combination of these.
The thermal type can false trigger as the room changes temp, or when the sun light hits it, or when the furnace comes on and a stream of heat hits it.
The electrostatic type is the least predictable and can be false triggered not just by static in the room (including things like dust, an insect, lightning or anything that can hold a charge) , but also by static on the power source (remember how you said your gfci trips?)
The remote controls get interference from a long list of other devices, TVs, cell phones, walkie talkies, garage door openers, kids games, etc, and therefore see a higher chance of false triggers.
What's important to keep in mind is that each of these types of controls consume power, even when the light is off. They have to be powered on in order to sense the temp or static or IR blast or radio signal when you are wanting the light to come on.
All of my led lighting has an old fashioned on - off switch somewhere upstream. When I store my RV these switches are off. You can turn them on and then use the switch or remote that came with the fixture,,,, but at the end of the trip, the toggle switches are off. No false triggers, and no trickle drain.
Larry