Time delay dpdt relay using only pot, relay, and cap (discreet components and no transistors)

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Time delay dpdt relay using only pot, relay, and cap (discreet components and no transistors)

I am trying to design a simple time delayed relay circuit that uses only a potentiometer, 5V dpdt EM relay, a single sufficiently large capacitor, additional resistors (if needed), and buttons/switches, powered by a 9V battery. The schematic below works to simply turn on an LED while a button is pressed and keeps it on for a moment. I have only been able to extend the time by adding more caps in parallel. I believe there is a simple solution to this logic problem that has the relay triggering itself almost as an oscillator, but when setting up as an oscillator I still can only vary the time by adding caps. How can I arrange and wire the components mentioned to allow a time delay of a few seconds to minutes, dependent upon a single potentiometer?

I thought a toaster's circuit would work, but most I see use a 555 timer or a pair of transistors and other components. Is there a simple way to use an RC circuit alone as a timing circuit without the solid state components?

I know how to do this using transistors and ICs, but that is not the point. It is an experiment to show a possible use of capacitors and RC circuits without first teaching about solid state components, ICs, etc.

The time delay can be delay ON or delay OFF.

Thanks