Found out about this jiggly cake store after asking a local Taiwanese.
I haven't heard of it before but it seems very popular with the locals. There were queues even though we went on a weekday afternoon.
There's quite a few different flavors and they go by weight rather than a fixed size. So you let them know how heavy you want your cake and they will cut for you an estimate of it.
The Old Time DelightsChanghua Store No. 462, Section 1, Zhongzheng Road, Changhua City