Horizontal Liquid Gauge with rapid response

Hi everything, I'm currently working on a project and could use some advise. My goal is to create a real-life "healthbar" that reacts to the lifebar in games. For visual aspects I want to go for mixture of liquid and LED setup looking like this:


The "bottom" part of the picture would be the only visible part and facing towards me.

I have tried a manual setup so far, consisting of a acrylglas pipe with a diameter of 20/16 mm (outer/inner). My plungers are currently two rubber rings with a diameter of 16 mm mounted on wooden sticks. This is air and water tight. To reduce the friction and make motion smoother I have used detergent. The plunger move quite smoothly with that, although I may switch to a liquid with lower viscosity.

The next step would be the automation of the plunger movement. This is the part I'm mostly lost at. The plunger needs to move a distance of ~15cm. Given that life in a game can change quickly, it would need to move that distance in approximately 0.5 s (faster response would be better). The liquid to be displaced would be about ~30 mL.

I have looked at linear actuators but found most of them to be very expensive for a small project and quite large.
Linear stepper motors may work but I'm not sure if they can response fast enough.
I was recommened solenoids but as far as I can see they are only meant for small displacements.

To summarize what I'm trying to achieve:
~15 cm displacement of ~30 mL liquids.
Response speed: 15cm/0.5s
Cost: ~15€
Bonus for low noise

Very tricky to achieve with that budget I'm afraid. How do you plan to get your game to tell you the current life level?

I'm not quite at that step yet, but for now my plan is to use either APIs (common in MMOs) that allow me to access the values I need, a graphic observation approach (e.g. measuring the length of a healthbar compared to the maximum length) or, although this approach might be the most difficult one, access the health value saved in the RAM similar to how some cheat programs do it (e.g. Trainers)