I was heading down the road of trying to sort this from what is standard, ie it could be that there is a fault and that the degree of flashing of the tail light is unacceptable even taking into account the drain a standard relay introduces. I still think this is a sensible investigation at this stage.
However I do like the suggestion of introducing a flasher relay with much less draw from the battery, an electronic one rather than a bi-metal strip with heat coil. I have found this, purpose built and not an led version...what do you think?
http://www.autoelectricsupplies.co.uk/product/710