Voltage divider for SSR input
Can I use a voltage divider to allow a 14V to 55V power supply to be connected?

A voltage divider sounds like it could work, yes.

Can I use two 4K resistors as a voltage divider

You mean 4 kΩ, not 4 K – 4K means &quot;four Kelvin&quot;, and that's damn cold, but not a resistance. &quot;k&quot; like &quot;kilo&quot; is written with a small letter up front.
Let's see: 14 V / (2· 4 kΩ) = 14/8 mA, which is a little less than 2 mA.
Your SSR will potentially draw much more current than your voltage divider does in itself, so the upper and lower resistors will experience a very different current, and the divider is a loaded divider.
That won't work. You need to use much smaller resistor values, so that the current through the divider is so large that adding the current through the SSR doesn't matter. A factor of 10 to 100 larger current is usual.

The load side of the SSR is a 12V drop down regulator.

That doesn't sound like an application for an SSR at all – simply control the regulator. Practically all regulators I can think of have something like an &quot;enable&quot; pin, or some other low-effort method to control them. You can either directly control that bin (single transistor), or if you actually need the galvanic isolation, with an optocoupler.
If your regulator doesn't have that, replace the regulator with one that has, instead of adding an unnecessary SSR to your system.