Running on tea cakes

Is anyone familiar with the phrase "running on tea cakes" to describe an unreliable clock?

What can you tell me about it? My father used to use it, but no-one else I ask seems to have heard of it.

I am guessing. The image I get is a delicate, perhaps poor, lady who lives on tea and toast. Or tea and teacakes. Food that doesn't have a lot of substance. Doesn't really give an energy boost.