I'm looking for a symbol that looks like two forward slashes in succession. Of course I can just enter two slashes like this: // but I would prefer a single symbol with these slashes very close together. I tried to google it, to no avail.
You appear to be looking for COMBINING LONG DOUBLE SOLIDUS OVERLAY which you can just enter directly. If you really want to use an entity then it is ⃫.
<p> ⃫
<p>⃫You might find font support for it is weak though, it is an obscure combination of diacritical marks.