The Bill was later passed, also unanimously.
Ministers will be allowed to flesh out the detail of the rules by regulation under the amendments, with parliamentary business minister Jamie Hepburn saying the regulations will be in place ahead of 2026, subject to parliamentary approval.
Another amendment from Mr Simpson was also passed, which allows ministers to ban councillors from sitting as MSPs, with a decision to be taken after a consultation.
Mr Simpson said he was spurred to press his amendments after SNP Westminster leader Stephen Flynn – who he did not name in the Holyrood chamber but made clear to whom he was referring – announced plans to seek a Holyrood seat and sit in both parliaments until the next UK election.
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Mr Flynn has since walked back from that pledge after a backlash from across the political spectrum, including within his own party.
It also emerged during the debate that the SNP has banned MPs from standing for Holyrood in 18 months’ time unless they first resign their Westminster seat, according to Mr Hepburn.
Mr Simpson said: “This is not a cosy club, this is a Parliament, this is not a second-rate chamber to be used as a part-time hobby, this is a serious Parliament, and members should be fully focused on their work here.
“Being an MSP demands our full attention, it is a full-time job, we make laws for the people, not to protect the vested interests of individuals or parties.
“The amendments I am proposing today stand up for this Parliament and the standing that it should enjoy – double-jobbing should be consigned to history.”
Scottish Green MSP Ross Greer said his party supported the amendments because being a member of any Parliament is a “full-time job”, adding: “The job is a privilege, a huge privilege, but it’s also immensely challenging, and it’s the kind of challenge that requires dedication to the role, a level of dedication I think we would all recognise our constituents expect from us.”
Along with the ban on double-jobbing, the Bill also makes provisions that will allow foreign nationals with limited leave to remain to run for office while barring sex offenders from holding office, along with those who have been convicted of a crime which includes hostility towards politicians or electoral staff.