For egg and milk you should be able to use one of the various allergen tests - you can get swab kits and/or have analysis done at external laboratories. Not sure who to recommend in Australia, although Eurofins are ubiquitous and can do this: https://www.eurofins...u/food-testing/
Theoretically you might be able to use this for the fish component too, although whether this will be useful is a more difficult question - certainly the view in the EU seems to be that isinglass isn't likely to be a significant source of the protein primarily responsible for allergies to fish, as it's exempt from allergy labelling here. An overview here: https://efsa.onlinel...n (NDA, 2004a).
For the beef gelatine I suspect the considerations will be somewhat similar. You might find that some of the meat speciation testing could be adapted to at least confirm whether there is any detectable presence of beef, but whether this tells you anything useful is going to depend on a number of factors.
It's perhaps worth asking what the "vegan" claim means in your case - is this for a retailer with a set standard that you need to meet, or a brand that "just" needs to comply with a regulatory requirement around the claim (which may just be about ensuring it's not misrepresented, in the absence of a formal definition of vegan)?
In general we're finding that the retailers here approach this very much in the same fashion as a "nut free" claim, whereas the regulators and indeed the Vegan Society seem to take a more considered approach - it's about not using ingredients/process aids derived from animals, and doing everything reasonable to minimise the potential for cross-contamination.
In that type of situation you could perhaps use the tests that are available (e.g. egg, milk proteins) and take the position that these are used as "markers" for the overall performance of the cleaning and segregation controls?