This is a zombie, so I cannot check the options.

As an adjective, both the GPC and Geiriadur yr Academi show rhan-amser as hyphenated, as is common with 'part-time' in English:

• 'a part-time job' should be swydd ran-amser - with the soft mutation of the adjective because it follows a feminine noun.

It may have been entered onto the database with a typo of * rhan-amser and then been deleted because of that.

[Note that the ll-, rh- exception does not apply in this case - that 'weak' soft mutation comes after:

• y (when used as the definite article)
• mor/cyn (when used meaning 'as, so' with equative adjectives)
• un
• yn (before adj or noun).]

It should be "Swydd rhan amser" since even though "Swydd" is a feminine noun "Rh" and "Ll" do not mutate softly in this instance.