the only real info i have on this thing is here:
NS72450/NS84450/NS96450 | far-driver where it shows brake high connected to a 12V converter. the manual as a pdf here:
https://www.far-driver.com/wp-content/uploads/Fardriver-controller-Manual.pdf also shows 12V in the description on page 5.
I poked around and while I find references to a few people on the web that have used "battery voltage" on that pin, they don't specify which controller brand or model they used, or what that voltage actually was, in the post / page linked in the websearches. They might say elsewhere in their project stuff, but I did not peruse that.
Most just say they used 12v, if they say what voltage they used at all.
You could ask Nanjing Fardriver themselves if you can get any response from them, and you can get a real answer instead of a parrot-back of the manual info. :/
My initial idea was to run everything at battery voltage and then put a 12V converter directly onto this pin. the issues i found here are
1) when the input voltage is removed from the converter the output still hangs at 12V for a second, meaning the after i release the brake lever the motor will still be cutoff.
Instead of a second DC-DC, you could use a "linear regulator", like the 7812, and no capacitor on it's output (so it just dies instantly to zero at input power loss). But IIRC the max input voltage on those is 30v...so you'd have to drop the DC-DC's output (from the brake lever to the BH pin circuit) down below that first.
Another option is a 12v zener diode, and a resistor. the resistor goes between the brake lever output and the zener. the zener goes from the brake high input to ground, and limits any input to a max of the zener rating, and voltage drops to zero as soon as the input goes away..
Like this example for a 9.1v zener. In your case the current needed for the BH input is virtually zero, so you don't need a low value resistor, and can use the max value to provide whatever current the zener requires for regulation per it's datasheet.
You'll have to check the math for this, but this is the google search AI output for the values. It used a 30ma example, but you don't need even a hundredth of that, I'd bet. You could compromise for a 1mA max output and figure out the values for a 30x higher resistance. You don't need or want any capacitors. Just hte zener and resistor.
Calculation Example (for a tiny 30mA load):
- Voltage Drop across R1:

36V−12V=24V36 cap V minus 12 cap V equals 24 cap V
.
- Resistor Value (R1):

24V/0.03A=800Ω24 cap V / 0.03 cap A equals 800 cap omega
(use a standard value like

820Ω820 cap omega
or

1kΩ1 k cap omega
).
- Power Dissipated by R1:

24V*0.03A=0.72W24 cap V * 0.03 cap A equals 0.72 cap W
(use a 1W or 2W resistor).
- Power Dissipated by Zener (D1):

12V*0.03A=0.36W12 cap V * 0.03 cap A equals 0.36 cap W
(use a 0.5W or 1W Zener).
The relay (DPST, 2P to keep the 12v and 36v separate, but you only need on off so 1T) plus the zener would fix boht the lever and BH pin having ot deal with higher voltages.
No second upconverter needed, etc. Can probably be built into a sugar-cube-sized "deadbug" configuration, siliconed up, and stuck wherever is convenient.