Looking at the above photos I see similarity to Needhams side lever and a gun that looks like a Scott ,but never seen a side lever version .This could be that actions were bought from one maker and finished by another.
There were numerous patents , provisional and full , improved patents , people claiming patents and those marking actions as patent even if it was not their patent . Add in that there were many short loved actions and those that copied patented actions , where the patent had expired or never taken beyond a provisional . It is fact that many patents granted at this time would not really have stood up to a court case as they were merely slight modifications of others .
As to the advantages or disadvantages the fact that they went out of use almost entirely says something for there popularity .
That said if you have missing or damaged thumb a side lever can be the answer to your problems it can be used with the heel of the hand as can be for a left handed person who finds a conventional top lever difficult.
