In these days of instant communication I don't know if the situation of ‘getting a dizzy' or being ‘stood up' can still happen but being ‘dizzied' or being stood up was a humiliating situation for persons of both sexes. 

The first example in The Dictionary of the Scots Language (dsl.ac.uk) is from 1958 in Cliff Hanley's autobiographical Dancing in the Street where he cites the plight of some poor, rejected friends: “Sometimes people who hadn't been able to get into the pictures or who had been dissied by girl-friends, came up to sit at the fire and talk.” Peter Mason, nearly 30 years later in his glossary specifically of Glasgow speech C'mon Geeze yer Patter (1987), gives the example: “Ah wis black affronted gittin a dissy at Boots's coarner.”

Michael Munro in his collection The Complete Patter (1996) gives both example and definition: “If  you make a date with someone and then fail to turn up you are said to have given that person a dizzy: ‘What's up son, did the lemon curd (burd) gie ye a dizzy?'” He also gives the same suggested etymology as DSL saying that it is likely a shortening of disappointment. 

However, getting a dizzy does not only happen in the West. SLD's Word Collection has the Edinburgh example: “Ah wis dizzied at Binn's Corner.” In Edinburgh's West End the corner site of this department store (now Fraser's) was a popular place for trysts. 

Dizzy Corner as mentioned above in Peter Mason's example does still seem to be current in the collective memory of Glaswegians: “Most Glaswegians still call it Dizzy Corner, the spot where, in gentler times, stood-up youngsters waited for their missing dates under the clock at Boots.”

Scots Word of the Week is written by Pauline Cairns Speitel of Scottish Language Dictionaries