Falkirk Sheriff Court heard that James Lynn-Wilson, 49, had made an "angry, erratic and abusive" call to Police Scotland.
A call handler said she "felt quite sick" after taking him to mean that he was going to take a gun to the address in Bridge of Alllan where the MSP, Conservative Stephen Kerr, lived and do what Hamilton did at Dunblane Primary School in the 1996 massacre.
Police were scrambled and Lynn-Wilson was arrested on a bus in Bonnybridge.
He walked towards a female cop repeating over and over again he was going to go to Mr Kerr's address and do what Thomas Hamilton had done.
The incident, in July 2021, was the second time in seven months that Lynn-Wilson had phoned the police mentioning Hamilton's name and making threats to go to Mr Kerr's house.
In December 2020 he rang police and gave his name, but added "some people called me Thomas Hamilton".
Police found Lynn-Wilson, "agitated and quite aggressive" close to Mr Kerr's home.
At a jury trial in March, Lynn-Wilson, of Denny, initially denied two charges of threatening and abusive behaviour but changed his plea to guilty.
Sentence was deferred until today for reports, which revealed a psychologist had found Lynn-Wilson had "no empathy".
Lynn-Wilson, who represented himself, said: "They can't fix that."
He asked the court to impose a Mappa (Multi-Agency Public Protection Arrangement) order, which he said he'd had previously, or to arrange for him to be put to sleep - understood to be a reference to euthanasia.
Sheriff Simon Collins QC imposed the three year jail term, backdated 11 months to allow for time already spent in custody, and ordered him to be subject to social work supervision for 12 months after his release.
He also imposed a non-harassment order, forbidding him from approaching or contacting Mr Kerr or his wife Yvonne Kerr for ten years, and forbidding him from entering the entire town of Bridge of Allan for the same period.
Sheriff Collins said: Both these offences related to your continuing, and as far as I can see, obsessive, fixation on the harassment of Stephen Kerr and his family.
"I've read the criminal justice social work report which suggests that you do not regret these offences and you have neither the intention nor the ability to modify your offending behaviour.
"You present a high risk of re-offending and a custodial sentence is inevitable, not just for punishment but for the protection of the public and Mr Kerr and his family."
He also recommended that on release he should be subject to a Category 3 Mappa referral - reserved for dangerous offenders who are considered to pose a risk of serious harm to the public.
The court heard Lynn-Wilson was on bail at the timeand had previously been jailed at the High Court in Edinburgh for stalking Mr Kerr.
In 2016 the High Court heard there was a history of animosity by Lynn-Wilson towards Mr Kerr, after Lynn-Wilson was excommunicated from the Church of Jesus Christ of Latter-day Saints in 2004 for "conduct unbecoming" towards the politician, a church elder.