The 8-pin or 9-pin male connector on a generic (i.e. mostly brands that are from China and Tawain like Bafang, Kunteng and Lishui) ebike controller is meant to connect a 1to4 cable (for the 8-pin) or a 1to5 cable (for the 9-pin). A 1toX cable (where X is a number) is a cable with a big connector on one end that connects to the controller and X connectors on the other end that connect to cockpit accessories.
The 1to4 cable is meant to connect a throttle, the left brake sensor, the right brake sensor and the HMI (human-machine interface which is usually an LCD or a more basic LED display).
The 1to5 cable is meant to connect the same things as the 1to4 but adds an extra connector for a headlight (probably the extra brown wire you are referring to). The light needs its own dedicated power wire since you can usually turn it on or off with the HMI.
If your new controller has an 8-pin connector, you simply need to buy an 8-pin 1to4 cable. Controllers with an 8-pin connector will usually have a separate wire for the headlight but some does not have any. Those cables are fairly cheap, so you are probably better off buying the right cable than trying to modify your old one.
A word of caution
The pinout of those cables is not standardized. While they seems to loosely follow one, there are known exceptions. The green 5-pin connector for the HMI can be different between Bafang and Lishui/KT. Here is a picture from the EggRider v2 display compatibility page:
Also, some brake sensors use the yellow 3-pin connector, while some use the red 2-pin connector.
Finally, there are two main types or waterproof controller side connectors for the 1toX cable (I am not talking about the number of pins here). It can be one from the HiGo Main Signal series (or compatible from other connector brands), such as the 8-pin Z812 which is mostly found on Bafang controllers:
or a connector that is similar to the 2-3-4-5-6-pin HiGo Mini B series, such as this 8-pin which is mostly found on KT/Lishui controllers: