HiCustomer Thank you for asking your question on Just Answer.
Here are the instructions to replace the core.
REMOVAL & INSTALLATION
See Figures 1, 2, 3, 4, 5, 6, 7, 8 and 9
Disconnect the negative battery cable.
Position a drain pan under the radiator, open the drain cock and drain the cooling system to a level below the heater core.
Plug the heater core tubes to avoid spilling coolant in the passenger compartment during removal.
Disconnect the heater-to-engine coolant hoses from the core tubes on the firewall, in the engine compartment.
Fig. 1: Exploded view of a common heater core and case assembly
Fig. 2: If necessary, loosen and remove the under dash cabin light retaining bolt
Fig. 3: With the bolt removed, the light and housing may be repositioned out of the way
On some early model vehicles, the cabin light mounted under the dash may interfere with cover removal. If necessary, loosen the retaining bolt and reposition the light housing with the wiring attached.
From the passenger compartment (under the dash) remove the heater core rear case cover-to-cowl screws, then remove the cover from the vehicle.
On a few of the early model vehicles covered by this guide, some of the heater core cover screws may be partially/fully covered by the dashboard. Be sure that all are removed before attempting to remove the cover. If necessary, unbolt and reposition all/part of the dashboard for better access.
Remove the straps or brackets from each end of the heater core.
Carefully remove the heater core from the cowl and case.
Insert the heater core into the case, taking care not to damage the tubes as they are inserted through the cowl.
Install the straps or brackets to the ends of the heater core and secure using the retaining screws.
Install the heater core rear case cover and secure using the retaining screws.
If moved for access, reposition and secure the dash mounted cabin light and housing.
Connect the heater-to-engine coolant hoses to the core tubes.
Connect the negative battery cable, then properly refill the engine cooling system.
Run the engine at normal operating temperatures and check for leaks.
Fig. 4: Loosen and remove the rear case cover screws
Fig. 5: Remove the rear case cover for access to the heater core
Fig. 6: Loosen and remove the core strap/bracket retainers
Fig. 7: Remove or reposition the straps/brackets so the core can be removed
Fig. 8: Most cores are retained by straps/brackets on both ends; don't forget to loosen all retainers
Fig. 9: Carefully withdraw the heater core from the case
If this helps, please click accept. If you have more questions, just let me know.
Take Care, Greg A.
Hi again and thanks for the accept.
As I always say, there is no stupid question, except for the one you have but don't ask.
The instructions do not mention anything about removing glove box. But in some cases, it might give you a little more room to work with. I know I like to have as much space as possible to work on things, especially under the dash.
It has been a long time since I have worked on this particular year of vehicle, but I seem to remember that there was plenty of room without removing the glove box. So you shouldn't have to remove it for this particular task.