Hi, I belive we have already answered your questions via email but I thought it would be useful to post our response here incase others are have the same question!
The timing is set by three components: two resistors and a capacitor. There's a great online 555 calculator that lets you put in different values to see the result:
If you look at the schematic shown on that page, you'll see the two resistors are named R1 and R2, and the capacitor value is C. There's also a capacitor from pin 5 to GND, but don't change that. It's not related to the timing of the output. Only the parts on the left of that schematic are relevant to the timing.
Now compare the schematic on that page to the schematic of our module. Putting the two schematics side by side, the equivalent parts are:
R1 on calculator = R1 and R2 of our module, depending on jumper setting.
R2 on calculator = R3 on our module.
C on calculator = C3 on our module.
So for the default values, you can put these into the online calculator to replicate how our module should behave:
Capacitor (C) = 100 uF
Resistance 1 (R1) = 4.3 megaohms
Resistance 2 (R2) = 4.7 kilohms
Make sure you change the units drop-downs on the right to match.
You'll see a result that shows about 298 seconds as the period, and time low as 325ms.
Right, now we're set to try changing values to make it work for your situation. The relevant value to change is Resistance 2 (R2). Try changing it from 4.7k to 10k, and you'll see that the period changes very slightly but the time low jumps to 693ms.
Make it 15k, and the time low goes to over 1s. That's probably the sort of period you'd like, in order to fully energise the relay and make absolutely sure the board is reset.
So, going back to our watchdog timer module, the "Resistance 2 (R2)" in the calculator is actually equivalent to resistor R3 in our circuit.
To replace that resistor with a higher value, you have a couple of options. You could remove it entirely, and put another one in its place. Or it may be slightly easier to cut the track that comes off the top of the resistor where it runs diagonally down to the right to the 555, and then solder a new resistor between that 555 pin and the adjacent pin.