In the main door bells are 4, 8, 12, 16 or 24 volt, the transformer/power supply often has the option to select the voltage, and the older units are normally 8 volt at 1 amp, which is ample to supply an LED lamp, being 8 watt, but LED lamps tend to be 12 volt, also the bell wire is not continuous rated, neither is the transformer, with the old ding dong bell some one at the door holding their finger on the bell push, or it getting stuck could burn out the transformer. They were often rather Heath Robinson set ups.
I clearly don't know how yours works, so can't tell you best options, but remember my parents house, we could see the transformer, and we could see the bell, and we could see the bell push, but what wires connected them and where they run was completely unknown. It clearly took some odd route and they were long and thin, as when we tried to use them to power a 12 volt DC bell push and intercom the volt drop was too high.
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