Electronic – MAT12 matched pair transistor substrate connection

Use 10kΩ for R3.

I didn't look up a BC547, but if that's a typical small signal transistor as it should be, figure a gain of at least 50. 6V supply minus 700mV B-E drip leave 5.3V accross the resistor. 5.3V / 10kΩ = 530µA. Times the gain of 50, and that can support over 25mA of collector current. That's well more than any reasonable digital input will require, even if it has a pullup connected.

As others have said, you may need a pullup if whatever you are driving doesn't passively make the line go high. However, make sure the pullup goes to same voltage as the power supply of whatever will receive the digital signal. Your supply is 6V, which is probably higher than the receiver's supply. That could cause the receiver to not work or even to damage it if its power voltage is significantly lower.

The transistor is jellybean Chinese PNP transistor. The specs (and even the pinout) vary somewhat from maker to maker- no JEDEC standardization here, but it's broadly similar to the Fairchild SS8550. They seldom fail if not abused.

Anyway, the thing under the blob is an IC chip (Chip-On-Board), and chances are very good that's where the problem lies (quite possibly in the wire bonds to the chip). In which case, the unit is not economically repairable. That construction technique is not particularly good (reliability-wise) for this kind of application but it is very cheap in high volume.

You could always hack in a mechanical switch (toggle or whatever) across the transistor and ignore the electronics. It's mostly there to allow an almost free momentary switch and allow blink modes. I'd try to disconnect the chip itself - I find that the one I have slowly drains the 4 AA cells whilst allegedly off. Or if you're ambitious beyond all reason, hack in a small microcontroller to drive the transistor.