Usually the 3 Pin Flasher Cans are for a system that has a single Repeater Lamp on the dashboard, or on the end of the Blinker Stalk, like the MKI Minis for example.
The 2 Pin Flasher Cans are for a system that has 2 Repeater Lamps on the dashboard like all the later Minis.
The original metal can type Flashers (in 2 and 3 pin) are a thermal type of unit that needs the load of the Lamps to make them Flash.
The 2 Pin types use the external (Front and Rear) Indicator Lamps for this load.
Check what type of 3 Pin Flasher Can you can get as there's 3 types I know of, there is one type that won't work here.
Check what markings are on the Terminals.
Type 1 - Terminals marked X , L and KP or could be 15, 54 and KP or 49, 49a and C;-
One of these 3 Pin types used these external Lamps for the Load and some used the single Repeater Lamp for this purpose (so in this type, there's 2 styles) . If it is or the Former type, then these will work without issue, just check which wires are going to what Terminal. They need to be (Dark) Green to X or 15 or 49 Terminal, Light Green to L or 49a Terminal. Ignore the KP or C Terminal.
Type 2 - Terminals marked X , - and L or 49, 49a and 31
These are a 3 Pin types that need the X or 49 Terminal connected to the Dark Green wire, - or 31 Terminal connected to Earth, and the 49a Terminal connected to the Light Green wire. These will work, but you'll need to add in the Earth wire.