The Miller electrics on your bike may be a problem for several reasons, among which the following.
1. They are now old & therefore more likely to be unreliable because of their age.
2. Previous owners may have fiddled with the electirics, doing goodness know what!
3. Parts are much harder for Miller (compared to Lucas) because of their rarity.
If you want to keep the Miller electrics it may be possible to rectify the current from the AC of the alternator to DC for battery charging, & fit a battery for your brake light. You won't need a much output as you can use LED bulbs which consume very little current.