Both of these threads on wall ties are very difficult to get your head around. It is very difficult to diagnose on a description only. Photo's would help.
Anyway, here are my thoughts:
Bulging of gable ends could be due to insufficient ties to to roof structure, allowing the wall to lean outwards (as there are no corners to tie it in). Alterations to roof structures such as loft convertions can create additional or accentric loading to walls causing bulging.
Early cavity walls (1920-1940 ish) are very hit and miss. Cavity sizes vary from house to house and even on the same house. These early cavities were often tied together using headers. These are sometimes visible as they sit back slightly from the face (on tight cavities). On wider cavities, they may not be visible, as the tie brick is set further back in the wall and faced with a thin header to enhance appearance.
As mentioned by tim00, early ties were large and seemed to be put in when the bricklayer remembered. Generally if ties are rusting through, you may be able to see a slight stain on the joint where the tie is, or a slight hairline crack as the rust causes expansion.
My advice is to cut a brick out of the wall where the bulge is and have a look for yourself. This will tell you if it has a cavity or not, size of cavity, type of tie used and the condition of them. Then replace the brick.
This information is based on my own experiences. Hope it helps.