External Battery Mount (deprecated)
This Shimano SM-BMR1 / SM-BMR2 external battery mount was used with the SM-BTR1 external Di2 battery all the way until Shimano released the updated BM-DN100 battery mount.
Just like the later model, the older BMR1 / BMR2 come in different sizes, a long and a short version. Which one you need depends on your frame mounting options.
The short (-S) version is generally mounted underneath the bike, below the chain stay for example.
The longer -L version usually screws into the down tube bottle cage holes and allows you to install a bottle cage and an external battery.
SM-BMR1 vs SM-BMR2 vs BM-DN100
The SM-BMR1 and SM-BMR2 are basically the same device. The '2' version is newer and is of better built quality. Apparently there were some waterproofing issues with early SM-BMR1 models.
In case you're thinking of installing a D-fly or wireless unit - only the BM-DN100 will allow for BluetoothLE communications. This means that the SM-BMR1 / BMR2 only support ANT using the SM-EWW01 D-fly and SC-M9050 display.
The updated BM-DN100 is required in order to use the EW-WU111 / EW-WU101 / SC-MT800 / SC-M9051 and connect to mobile phones.
Updating the SM-BMR1 / SM-BMR2
While I haven't been able to confirm this, I do have a corrupted/broken SM-BMR1 that cannot be restored using the SM-PCE02... so there is probably some truth to this.
Also, some older Shimano documents state that the battery must be removed when you update these units.