I think the biggest problem with grappling with a concept of time is the tendency to try to think of time as some mixture of space and time. I think the biggest source of confusion has arisen from the use of the term, space-time--as though space and time are somehow mixed. The 4th dimension is not time, nor is it some kind of mixture of space and time.
So, one could first imagine the universe as a 4-dimensional space populated by 4-dimensional objects. The whole 4-dimensional universe is just there--all at once. Don't even bring time into the picture initially. This assures that you begin with a distinct separation of space and time into two separate concepts. This concept goes by the name of "Block Universe" and was suggested by Einstein's colleague, Kurt Godel (many physicists feel like Einstein embraced this concept--he just never liked to discuss it openly because of some of the bizarre implications).
Now, after envisioning a static 4-dimensional universe, then put in consciousness moving along the 4th dimension at the speed of light. So, in some sense--at least for us 4-D universe inhabitants/observers--the time comes in with consciousness.
Special relativity directly implies such a 4-dimensional block universe. Thus, the 4th dimension should not be thought of as a time dimension. It is a physical spatial dimension in the same sense as the other three spatial dimensions.