"Have X, will travel" - what kind of grammar is this

Solution 1:

It originates from the title of an American television series that was produced from 1957-1963.

The title was a variation on a catchphrase used in personal advertisements in newspapers like The Times, indicating that the advertiser was ready for anything. It was used this way from the early 20th century. A form common in theatrical advertising was "Have tux, will travel," and CBS claimed this was the inspiration for the writer Herb Meadow. The television show popularized the phrase in the 1960s, and many variations were used as titles for other works such as Have Space Suit—Will Travel by Robert Heinlein.

Advertisements, like newpaper headlines, frequently would drop words to make them more concise. The more grammatically correct sentence would be "I have [my own] gun, and am willing to travel."

Solution 2:

There is perhaps an earlier source than the one referred to by Bob Hope in his 1954 biography, though it might not have the same form as the now well-known snowclone. From Wikipedia: Snowclones ... Have X, will travel

Have Gun – Will Travel, 1959

The earliest known literary mention of the template "Have X, will travel" is the title of the book Have Tux, Will Travel, a 1954 memoir by comedian Bob Hope.

Hope explained that "Have tuxedo, will travel" was a stock phrase used in short advertisements placed by actors in Variety, indicating that the actor was "ready to go any place any time" and to be "dressed classy" upon arrival. The use of variations of this template by job seekers goes back considerably earlier, dating to at least the 1920s, possibly around 1900, in The Times of London. [Partridge, Eric (1992). A Dictionary of Catch Phrases: British and American, from the Sixteenth Century to the Present Day. pp. 118–119]

Variants of the snowclone were used in the titles of the 1957 Western television show Have Gun – Will Travel, Robert A. Heinlein's 1958 novel Have Space Suit—Will Travel,Richard Berry's 1959 song Have Love, Will Travel, Bo Diddley's 1960 album Have Guitar Will Travel, The Three Stooges' 1959 film Have Rocket, Will Travel and Joe Perry's 2009 album Have Guitar, Will Travel.

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As mentioned, the template is known as a snowclone ... a series of idioms having the same form. These idioms are of the extragrammatical variety (and may be analysed as having double subject deletion). They don't have standard grammar, but are acceptable by common usage. Your extended explanatory sentences (2) / (3) are easily deducible, perhaps substituting 'where X will almost certainly be required'.