How to target people in the 5th-8th slot?

Hey there, I'm a White Mage, I play on the PC, I use the keyboard, and a game mouse with 12 keys, meaning that I have quick access to all 12 numerical buttons, and switching which hotbar to use, however I still cant reach players 5-8.

I read online how players trick their way with revival spells having Macros that go over all teammembers
<t>
<2>
<3>
etc
All to just run through everybody until they find someone dead and revives him, however this can't apply to normal spells where stuff like Cure, Regen, Esuna do not have a restriction where the spell won't be cast if not needed. I looked up some guides online, and people mention <mo> as in, the mouse-over targeting option for that. I tried it, I tried to use that on a bunch of stuff, but whenever I forget it and don't have my mouse over anyone, it just targets me. Now true, this might just be an initial difficulty, and something that I could get used to, but I felt like asking around first, to check if this is as common of an option as was advertised to me, or if there are better alternatives to begin with.

I'd appreciate helpful input

First, I want to make sure you're aware that mouseover targeting works on the party/alliance list as well as over their character model. Some don't know that and are trying to heal exclusively via mousing over moving character models, which is nightmarish. That said -

I'm at work so I can't check the ingame options, but is there an option to disable auto-self-cast? I could have sworn there was, but it might be a different game. If there is that option, then a mouseover macro that's not moused over on anyone wouldn't automatically target you, it would just fail to cast anything. That might be what you're looking for. A few other things, though:

If desired, you could set up a macro as follows to attempt to cast on a mouseover, and if none is found then use your target.
/ac "Cure" <mo>
/ac "Cure" <t>

There are caveats to this. Macros can't be queued and will try to execute each command as fast as possible. Your casts will be slightly staggered compared to using abilities normal. Non-macro'd abilities allows skill queuing (Absolutely no wasted time from the end of one cast to the start of another). That's a significant downside for DPS, but on the healing side we have another thing to consider.

If you're spamming the macro to heal and your GCD is 2.5s, the <mo> line may try to execute before the GCD has expired, but the <t> line after. The <mo> line would fail right before your new GCD comes up, then the <t> line would execute, functionally skipping the mouseover and healing on your target. I saw this myself when I first started playing. I think I used a <t> line and a <mo> line, and a few times a night a heal I planned on the tank would go off on someone else (usually me). A...workaround to this is to have multiple lines of your intended cast, such as:
/ac "Cure" <mo>
/ac "Cure" <mo>
/ac "Cure" <mo>
/ac "Cure" <t>

This makes the situation above less likely to occur, but it's kinda a brute force method and if you don't have anyone moused-over will technically delay the <t> cast a very slight amount since it has to try to execute the previous lines of the macro first.

Macros are technically inferior due to the inability to queue them. At the same time, I haven't seen macro'd healing abilities stopping anyone from doing any content, and my personal testing with macro'd cure shows virtually no time loss from the macro, possibly because cure/cure II are 2s casts instead of 2.5, letting you start jamming that macro key a full 0.5s before the GCD has expired. Because we pre-heal tankbusters or various raid mechanics, we don't follow ABC (Always be casting) to a T since we have to delay a bit for those pre-heal timings, and this makes accrued time loss from macros less impactful. Regardless of what you choose to do, you're correct in that you've gotta get used to it. I don't know of anything out there that makes targeting mistakes less of an issue, save that potential option of disabling auto-cast if it does exist.

Edit: I'm also not sure what about your setup makes it hard to hit players 5-8 but not 1-4. Could you elaborate? As far as I know, most keyboard/mouse players are either clicking the party list names or something equivalent, like using mouseovers on them. Since you're asking about mouseovers I'm assuming you're not trying to target players via hotkeys (i.e. F2 = player 2, F3 = player 3), but that's an option too. You also mention swapping hotbars. I don't think this is common in most players mid-combat. I'm used to seeing multiple hotbars active with modifiers for each one, such as Alt+(1-0) for a second hotbar and Ctrl+(1-0) for a third hotbar. I haven't seen many players having one hotbar and rotating it around such that "1" on your keyboard might cast Cure, Esuna, or Stone depending on which hotbar you've scrolled to.

The keybind targeting options permit you to map party members and your own pet to keys. I've mapped myself to Numpad 1 and other party members to Numpad 2 through Numpad 8, and my pet to Numpad 9.

Using macros for things other than Asylum (in the form of <t> and <tt> macros) will likely be detrimental to performance. Macros increment only in whole seconds, whereas your recast time is almost certainly not integer seconds for any spell.

But it does seem strange that <3> works for you and <5> doesn't.

Could you elaborate on what you're trying to do?

You have several options, my go to, is using the f keys. they align with the party member slot, all the way to 8, so f1 targets the first on the list, f2 the second and so on. But in addition, if you can click the character model, that's available too, macros allow for mouse over, which works on the party list too, and there's also the fact you can just click in the party list to select someone.
For instance, I divide my targeting and buttons from 1-5 as things I press and 6 and above as a click, both on my hot bars and on my target keys. So if I need to target party member 7, I just click on them in the party list. Otherwise, I use the f keys, but each player comes up with their own style on how to do this. I hope that other healers here can give you their healing tips on what they use, because there is no wrong method.