the scheme argument of urlsplit/urlparse is completely broken.
here two examples:

urlunsplit(urlsplit("httpbin.org", scheme="https://"))
'https://:httpbin.org'

urlunsplit(urlsplit("httpbin.org", scheme="https"))
'https:///httpbin.org'

Fix: change urlsplit logic like this:
...
url, scheme, _coerce_result = _coerce_args(url, scheme)
scheme = scheme.rstrip("://") # this removes ://
...
i = url.find('://') # harden against arbitrary :
if i > 0:
    ...
elif scheme:
    netloc, url = _splitnetloc(url, 0)  # if scheme is specified, netloc is implied

sry too lazy to create a patch from this. Most probably are all python versions affected but I checked only 2.7 and 3.7 .