The cable attached to the signal output should be shielded and not too long, about 1 meter works well.
A BNC socket is easy to install in candy tin boxes and very robust, but smaller 3.5 mm audio sockets can be used as well.
BNC at the detector also allows the use of standard BNC cables for direct attaching to regular oscilloscope inputs.

Standard stereo/3-pin 3.5 mm jack to 3.5 mm jack audio cables can be used, but they should be short and shielded which is rare. Look for high-quality cables from a music/audio equipment store, e.g. microphone cables.

Search for TRS BNC cable or similar. The TRRS-to-BNC cables for headset sockets are quite rare but can be found, too. Ask the sellers directly if the cable is sold out. Send them the picture of the connection diagram below to make sure getting the correctly wired version.

• BNC to 3-pin/stereo jack (TRS) cable from Ebay, Aliexpress (alternatively: 2-pin/mono jack "TS")
• BNC to 4-pin/headset jack (TRRS) cable from Ebay

ATTENTION:
Please read the overiew below carefullty for deciding which 3.5 mm audio jack connector you need: 3-pin or 4-pin, TRS or TRRS!

3-pin versus 4-pin, TRS versus TRRS:

A 3-pin 'TRS jack' is required for regular mono or stereo sound inputs (like on USB soundcards, certain desktop computers or old laptops).
A 4-pin 'TRRS jack' is required for most integrated headset sockets of smartphones, tablets and modern laptops.

MIC = microphone-like signal => connect with the inner wire of the BNC cable/socket to the detector ouput (marked as 'signal' on the board)
GROUND = connect with the outer shield of the BNC cable/socket (marked as '-' on the board)

Important Note:
Certain systems, like all Apple hardware, switch only automatically from headphones mode (=output only) into a headset mode (=simultaneous audio output and input) if the detector is powered before plugging it in.
Few non-Apple PCs and laptops have flexible 4-pin sockets that could be configured in different modes, e.g.: headset mode (TRRS-style) or microphone mode (TRS-like, using only the tip and sleeve connections for the 4-pin socket). Please check your audio system settings of Windows or Linux very carefully in order to find out and decide which mode you want to use.

Further pinout drawings of typical TRS and TRRS connectors.

Since the crimping of BNC connectors onto shielded coaxial cables can be annoying, the easiest way for a BNC-based connection is to cut a pre-configured, 2-3 meters long, BNC-to-BNC (male/male type) cable in half. Then solder a 3-pin/stereo 3.5 mm jack onto the cut end of the coax cable. RG-174 coax cables have a rather thin outer diameter below 3 mm which makes them easier to attach and solder to the 3.5 mm jack connectors in comparison with more common and thicker RG-5x cables.

Recommended parts:

• RG-174 coaxial cable with BNC-BNC male connectors: Pomona Electronics, 2249-K-120 (3 meters to be cut in 2 halves => allows for making 2 cables)
• 3.5 mm 3-pin/stereo jack connector (TRS): Neutrik, NYS231BG
• Alternatively: 3.5 mm 4-pin/headset jack connector (TRRS): Cliff FC68124 (instructions below)

Smartphones, tablets, and modern laptops (e.g. Macbooks from 2013 and later) usually have a socket for 4-pin TRRS connectors, the one that headsets use. They use 4 pins to connect stereo earphones as output, one (mono) microphone as input, and a shared ground connection. This requires a 4-pin 3.5 mm audio jack connector, where the second ring (counted after the tip) serves as ground and the sleeve/shaft at the connector base is the signal input. See the "TRRS Jack" drawing in the image at the bottom.
Some old 4-pin headset sockets may require a reversed polarity. If the pulses are upwards instead of downwards pointing, simply swap the ground and signal connection at the second rind and the sleeve.

The circuit board must be powered in case of certain smartphones and laptops (Macbooks/iPhones/iPads) before plugging the TRRS audio jack into the headset socket. If the detector is not recognized as an external microphone, please check the values of R8, R9, C9, and C10. Those values must be exactly as specified and differ depending on which variant is built (electron-detector vs. alpha-spectrometer).

Soldering 4-pin TRRS audio jack connectors to BNC cables is not recommended for electronic beginners. Please consider buying ready-made cables instead.

Soldering a cable with a 3-pin/stereo jack connector (TRS):

Note how the center of the coax cable connects to the tip of the stereo/3-ping TRS audio jack (that is usually the left channel in case of stereo inputs). The middle ring is skipped and left un-connected but is better to be present instead of using a mono/2-pin audio jack. Certain microphone input sockets, like the ones of CM108 USB Soundcards, apply a small bias voltage to the middle ring. This would be shorted to ground if using only a mono/2-pin audio jack and could affect the measurements (but in most cases, this is not a problem).
The shield of the coax cable connects the ground of the detector circuit with the sleeve of a stereo/3-pin TRS audio connector. See the "TRS Jack" drawing in the image at the bottom.

Readily configured cables are rare but can be found online. Search for "BNC 3.5 mm". Make sure to check for the required polarity at the 3.5 mm audio jack connector or modify it if need. Metal-cased 3.5 mm audio jack connectors are usually easy to open.