Electronic – How to generate a 555 fixed time delay even if trigger button is held on?

The description was a little ambiguous; this is how I interpreted it:

After the input reaches a certain threshold level (dotted line), the output goes high for 25 seconds.

The functions of a Schmitt trigger and a monostable need to be handled by two separate 555s. Luckily, you can get two 555s inside one 14-pin IC called a 556. Here is a circuit which uses the first half of the 556 as a Schmitt trigger, and the second half of the 556 as a 25-second timer. If you want a different value for the timer, change R3.

Note because of the typical tolerance of electrolytic capacitors, ±20%, the accuracy of the timer will be about the same assuming you use a 1% resistor for R3. If you want tighter timing, you can get a 10% tantalum capacitor, but they are relatively expensive ($5). They do make 5% tantalum capacitors, but only in surface mount packages.

When the input voltage is above 2/3 Vcc, the output of the Schmitt trigger goes low, triggering the monostable. When the input is less than 1/3 Vcc, the output of the Schmitt trigger goes high. Note that the TLC556, linked to earlier, has a Vcc range from 2v to 15v which gives a lot of flexibility in setting the hysteresis levels.

There are variations on this circuit, including adding a capacitor to the input and a voltage divider to change the trigger voltage. This article has lots more information.

If you had a resistor tied to the battery only, yes less current would be driven by that 1 MOhm resistor, but actually less heat is generated. Heat is generated from the power dissipated (as heat) by the part. So power is V * I which is (for a one resistor, one 12 V battery setup) 12 V * (12 V / Resistance) using I = V/R to calculate I. So as resistance goes up, power goes down for a constant voltage.

I don't know enough to reliably help you with your main problem, just thought I would contribute what I could.