Source of light
I imagine that the cause of the stars becoming dimmer is that some electrons are relaxing down before others.
This statement could be interpreted in two different ways, one incorrect and one correct. It could mean that electrons have an "on" state where they continuously emit light. That is not the case. Instead, they emit light once while going from an excited to the ground state. It could also mean that different electrons relax at different times. As electrons relax, the total number of excited electrons decreases. As a consequence, there are fewer excited electrons after some time, and as such fewer electrons that can emit at that later time. This is the correct interpretation.
Kinetics of decay
my thought is that the star should either be completely "charged" or cast no light at all, like a switch.
This is a conceptual model that goes against the OP's observations, so we already know it does not work this way, but the question is why.
To address this, here is a setup that does have the properties of a switch. I will use this alternate setup to compare and contrast. Take a star lit up by multiple light-emitting diodes (LEDs) powered by a battery. In LEDs, the electron flow continuously gets electrons into excited states, which then relax to ground states, giving off light. As a consequence, the LED will emit light until the battery is discharged to a degree that it no longer provides the necessary voltage. As a consequence, all the LED's will turn off at the same time.
Now let's compare and contrast with the glow-in-the-dark stars. They contain electrons that get excited in the first phase (shining light on them) and then they go back to the ground state once in a slow process that takes hours. You can measure the light emitted, as in this experiment:
Rather than all emitting at the same time (which would result in one flash of light) or emitting in a zero-order fashion (which would result in constant intensity that abruptly turns off when all electrons are at ground state), the intensity diminishes gradually, with the largest change at the outset.
This is not what we perceive when looking at glow-in-the-dark stars in a darkened room (probably because our eyes adjust continuously because the is no background or reference of constant brightness). Also, at one point we will probably fall asleep.
Mechanism at the atomic level
The Journal of Chemical Education has a nice article on this (Lisensky et al 1996, DOI: 10.1021/ed073p1048). Here is a quote from the abstract that connects kinetics with mechanism:
[J Chem Ed] The phosphorescence decay of ZnS:Cu fits a second-order equation, consistent with recombination of relatively equal populations of holes and electrons (n ~ p).
And as an aside, here is a diagram from Wikipedia (article: Light-emitting diode physics) showing how LEDs are continuously providing excited electrons and holes they can fall into: