R, 66 48 46 43 4038 bytes
function(s)identical!any(duplicated(rle(s)$v,unique(s)) This is a function that accepts the input as a vector of digits and returns a boolean. To call it, assign it to a variable.
It certainly isn'tNot the shortest but I thought it was a fun approach. We run length encode the input and extract the values. If the list of values is identical to the input withcontains duplicates removed,then return TRUEFALSE, otherwise return FALSETRUE.
Verify all test cases onlineVerify all test cases online
Saved 20 bytes thanks to MickyT, 3 thanks to Albert Masclans, and another 35 thanks to mnel!