I think I've got this figured out, then. (Partly because I need to read the magic-user instructions and not just the Illusionist ones.) Cracking off 30 years of dust and age...
First, the number of cantrips known in the spell book.
As quoted above, it's assumed most wizards set their cantrips aside and adventure with only powerful spells in their travelling spellbook, which is their justification for putting this in the unearthed arcana expansion. (That's not what you or I are looking to do, because they're fun and flavorful.) It says: "This assumes that the magic-user has, in fact, retained his or her book of cantrips - a tome as large as a good-sized book of higher-level spells." So, you still know all the cantrips you learned as an apprentice as long as you're willing to carry them in a spellbook. (It looks like we're doing a fast and fun game here, so encumbrance and spell-book-capacity are not factors Leitz is asking for.)
Magic User:
Illusionist:The number and types of cantrips known and recorded is determined by random use of the tables on page 30 of this volume. The exception
is the table of useful cantrips — those which are employed to make apprenticeship less wearisome. An apprentice has one useful cantrip for
each point of intelligence, and is allowed free choice from the list of 20 offered. For the other five categories of magic-user cantrips, the number
which may be known (selected at random) is as follows: reversed, 2-8; legerdemain, 2-5; person-affecting, 2-8; personal, 2-8; and haunting sound,
2-5.
By the book, we randomize a BUNCH of cantrips and keep them in our list.Illusionists have available to them all of the cantrips that can be learned and employed by regular magic-users, although an illusionist’s
capacityfor such minor magics is different in each category from that of a regular magic-user (see the list that follows). In addition, illusionists can learn and employ from 5-8 minor illusion cantrips, none of which are available to regular magic-users. Except where otherwise indicated, all properties pertaining to magic-user cantrips likewise apply to those employed by the illusionist class. The number of magic-user cantrips available to illusionists in each category is as follows: Useful cantrips: One per point of intelligence, up to intelligence minus 3; i.e., an illusionist with 18 intelligence can choose 15 useful cantrips from the magic-user list. Reversed: 2-5 Personal: 2-5 Legerdemain: 3-6 Haunting-sound: 5-8 Person-affecting: 2-5
[1d4+4] = 3+4 = 7 Illusion [1d4+1] = 4+1 = 5 Reversed [1d4+2] = 4+2 = 6 Ledgermain
[1d4+1] = 3+1 = 4 Person-affecting [1d4+1] = 4+1 = 5 Personal [1d4+4] = 4+4 = 8 Haunted sound, plus 14 Useful cantrips.
I'll happily go build that list. Looks like fun.
Second, casting the cantrips.
I don't know why my brain frizzled on that before. It is obviously as you stated - you sacrifice a 1st level spell and can memorize four cantrips instead.However, a magic-user may opt to retain up to four cantrips in place of one 1st-level spell.
Leitz' house rule that we don't have to memorize and can, in fact, cast on the fly is already a boon to us in this. It allows us a lot more variety in our activities, even given that we each only have 2 spells/day in the first place. I remember now why I loved cantrips in 1e.
As an illusionist, the cantrips are almost as effectual as the full illusion spells (the latter being needed mostly to cast at longer range or for extended time), so being able to cast x4 instead of x1 makes it far less debilitating as a low-level magic user.
So... I'm now pretty confident that's how it would work as-written. Magic-users are near-useless at low levels (which is probably why you and I both multi-classed for this quick campaign already). I always allowed house rules so that wizards could pick up extra spells-per-day for INT like Clerics do. If Leitz wants to consider making casters more useful party members he could either offer INT bonus spells, or allow X number of cantrips per day without consuming our only two actual spell slots, or allow unlimited cantrips with 1 per round (like 5e).
Spoilers! 