Electronic – Analog switch with a fixed state when not powered

Use any two different color LEDS reversed in parallel with a single R to limit current like 1k and connect across switch (to mechanical device).

Do you have +7 or -7V to load or +- V where V = 5 to 12? Latter I guess.

LEDs will be selected with polarity and protect themselves from excess reverse voltage .

Basically you want a 16PDT (electronic) switch. Look up analog multiplexers, that's how they're usually implemented. Here's for example the functional diagram from the datasheet of a 4PDT one:

You'll need use four of these.

You also need some additional memory circuitry to remember the state without power, like NOR flash, e.g. found in a microcontroler, if you want to completely avoid a mechanical way of remembering the settings.

And you can still find DIP packages for both analog multiplexers (e.g. BU4551 is the same type as the one above) and microcontrollers (e.g. ATMega328P aka arduino, or a smaller one like PIC12F617). You can find multiplexers with more (than four) channels on a chip, but usually not in DIP because they get large.