Tom:
You have already gotten most of the information you'll need, but as per
normal, I will put my quarters worth in anyway.
As was said, put the sealer tape on first to give the connection a good
solid water tight seal.  If the electrical tape goes on first, as john
mentioned, any gaps or spaces left by the tape will potentially gather
moisture, dirt, dust or what ever else might happen by.
The electrical tape is really not necessary on the outside at all, except
for perhaps keeping dirt and dust from sticking to the sticky outer surface
of the sealer tape.
I suppose electrical tape offers some amount of protection, but its so
minimal as to be useless.
So, don't put electrical tape on first, then the sealer...who ever told you
this was not using his/her collective grey sells in a productive manner.
However, any of the connections i put together, always have a good chunk of
sealer tape on them, as well as a wrap of electrical tape on the
outside...better safe then sorry I always say.
If the connection is going to be in a particularly wet location, such as
near the ground on a vehicle, or near the roof where water flows off, then
use plenty of sealer tape, at least two complete layers to insure all wraps
are over lapped.
Also, you should wrap not only the point of connection, but also the spot
where the coax enters the PL259connecter.  If you make this all one complete
continuous wrap from the same peace of tape, then the seal will be very
good.
You won't have any leakage problems as long as the ends of the tape or seal
are well sealed.
The tape backing is to keep the tape from sticking to itself on the roll, so
always take that off...since its just paper, with the first rain, it will
dissolve and cause large gaps in the tape and break the seal.
good luck.
I'd love to be able to outfit an RV with ham antennas...sounds like a fun
project.
73
Colin, V A6BKX