I played a High Elf Cleric during the classic era and actually did a large amount of solo leveling in old world zones, including a surprising amount of post level 30 soloing. In addition, although it is true that undead are particularly easy targets for clerics there are other old world spawns (most outdoor) which make easy targets. Although my memory is hazy considering I was in my teens and this was 10 years ago, I think this is how I did it-
8-13/14 in Unrest or Befallen in the Courtyard
14-17 in Oasis on Crocs
18-23 on Spirocs in Lake Rathe
By the time I could solo camp the 3 spot in Rathe (probably about 23-24) I moved to CT until my low 30s and then LGuk. I feel grouping during this time is critical because clerics really begin to shine as healers after lvl 24 and it is important to get a good amount of intense dungeon healing experience in before one hits a higher level. AE groups during this time in CT and LGuk are also awesome ways to practice the type of pre-healing/spam AE healing that becomes so critical later in raid and uber-mob situations.
During my mid to upper 30's I began camping the single specter spawn in the Feerrott, most likely when I got my lvl 34 spell ring. This bad boy can be pretty mean at first, however he is on a 5-6 minute timer which is ideal for single spawn soloing imo. At this point in one's soloing career it is essential to have Jboots. It is also super, super important to understand the function of the stun line of spells; it is to save you if everything else goes bad. However, with Jboots, divine intervention, root, and a couple of stuns (not to mention complete heal) it was actually very rare to get killed soloing. And of course, the highest perk of playing a cleric is that if you do die for whatever reason you can also just self-res and save yourself a huge headache and time loss.
In terms of killing the specter, I feel like I would root, nuke twice at a maximum distance, run, turn around root and repeat. Also, this spawn is close to CT and relatively close to Lguk so it is a great option if you are playing some off hours trying to grind away. I think this guy is decent EXP until 39-40.
Now, in terms of post 40 soloing there are some NPCs in the old world that work out. In particular I am recalling a few NCPs in OOT, a dwarf by some docks, guards (including the one in EC), and even by the upper 40s beetles in SolB or certain undead double/triple spawns in Guk. For outdoor, non-undead mobs in the 40s it is important to use the Stun line as much as possible but also always be ready to run with Jboots. I know for a fact that it can be done however. For indoor, dungeon spawns its better to stick with undead (even tho beetles are a nice mix-up) mainly and pick camps that have a low number of spawns and get some help breaking them up so you don't get overwhelmed.
At this point it is also important to mention that with a manastone cleric solo viability increases extremely. I believe it takes about 3 1/2-4 minutes to get to full mana, making clerics a potential solo machine in outdoor old world zones. However, I didnt have a mana stone until much later so it is not required.