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According to the article Media Throw Everything at the Wall to See What Sticks:

Witless college students demanded cyanide pills be stocked in campus health care clinics, on the grounds that Reagan was going to get us all nuked.

Is the statement factual?

According to the 1991 book Horrendous Death and Health: Toward Action :

Brown University students took significant action in 1984, before the Cold War thawing. The students voted to have the campus health center stock cyanide pills so they could easily commit suicide in the event of a nuclear war

and according to a Brown University webpage:

On October 12, 1984, a queue of students waited for over an hour in a line snaking from the winding staircase of Sayles Hall, out to the foyer with pictures of former presidents, and onto the main green, despite a broken voting machine and snappy cold weather. Over 1900 students showed up to vote on a referendum asking Health Services to offer cyanide pills in the event of nuclear war, which was a larger turnout than any other vote in recent history at Brown.

With weeks of priming in the news, in posters and demonstrations on campus, and a story on CBS, Brown students were ready to vote on the controversial decision. Arguments flared between cold, testy students waiting on line, and posters put up late Tuesday night likening the referendum to the Jim Jones' mass cult suicide were hastily ripped down by supporters of the SST.

57% of the student body who voted said that they were willing to see Health Services offer cyanide pills, and the world gasped in response. The vote seemed to be split along gender and political lines with 81% of females and only 53% males supporting the referendum. 80% of Mondale supporters voted for the referendum and nearly all Reagan supporters voted against. It was a shocking outcome, and the campus did not seem ready for what was meant by the result.

See also this 1984 UPI article.

Also, according to the 29 November 1984 article Cyanide Pill
Push May Harm Freeze Movement in Fiat Lux:

Attempts by students at Brown University and more recently at the University of Colorado to stock cyanide pills for use after a nuclear war may be doing the fading campus freeze movement more harm than good, some activists warn.

Last week—in the largest student vote turnout in six years—Brown students voted 1,044 to 687 in favor of a measure asking college officials to stockpile suicide pills for optional student use exclusively in the event of a nuclear war.

At the same time, Colorado student leaders voted to hold a similar referendum on that campus in late October.

No, not really. They were making a dramatic and hyperbolic gesture about the dangers of nuclear holocaust, but they were not seriously hoping to have pills handy for use.

In any event, organizers say their aim is largely symbolic: they want people to equate nuclear war with suicide.

"There are words we hear talk about when people mention nuclear war: survival, recovery," said Jason Salzman, 21, a junior from Denver who is one of the group's four organizers. "I like more appropriate words: suicide, death."

Still others supported getting the referendum approved for voting as a statement about free speech and democracy.

Mr. Salzman and Christopher Ferguson, 21, a sophomore from New Rochelle, N.Y., who is also among the organizers, said many students signed the petition to put the question on the ballot not because they supported the measure but rather "to let it get on the ballot in the spirit of democratic process."

It seems like the students voting were also aware of the symbolic motivations, as well.

Madeline Butcher, 19, a sophomore from Brunswick, Maine, said she would vote yes and hope the health service would stock the poison "to make everybody a little more aware of the reality of it all."

But Scott C. Ganeles, 20, a junior from Peekskill, N.Y, said he would vote for the referendum "just as an idea - just to put the word 'suicide' with 'nuclear holocaust.'"

NY Times Archive 10/11/1984: Brown Students Vote On Atom War "Suicide Pills"

Was it silly and more than a little foolish, to our eyes in the post-Cold War era? Perhaps, but many today do not realize the actual danger of those times, as well.

In any case, the idea that they wanted the pill available as a practical alternative, rather than making an attention-grabbing statement, is also overblown, as is the idea that college students were "clamoring" for cyanide. But that's not surprising, given the source.

Apparently so.

https://www.thecrimson.com/article/1984/10/22/grave-new-world-pbwbhat-were-1044/

October 22, 1984 WHAT WERE 1044 Brown University students trying to say last Friday when they voted that their university should stock cyanide pills to be used in the event of a nuclear war?