You're speaking with Dr. Michael Salkin. Welcome to JustAnswer. I'm currently typing up my reply. Please be patient. This may take a few minutes.
I'm sorry to hear of this with Murrisk, Win. The main considerations in such an elderly cat are cognitive dysfunction (senility) which has predisposed to inappropriate eliminative behavior and marking behavior most likely due to anxiety associated with cognitive dysfunction or perhaps a medical disorder heretofor undiagnosed. Pragmatically speaking, I'm going to discuss just one manner in which to address marking in an elderly cat.
Treatment involves two major considerations: 1) Remove the cause - easier said than done. You might have to be quite the detective to discern the stimuli for his inappropriate eliminative behavior 2) Prevent Murriskfrom returning to previously soiled areas by confining him to a very small area with the box and only allowed out when he can be supervised 100% of the time. When confined to a relatively small area, most cats seem to prefer to eliminate in the box rather than soiling the floor. It’s then a matter of confining him long enough for a consistent habit to become established. As a rule of thumb, one week of confinement is usually recommended for every month of soiling. Murrisk should be removed from the confinement area as much as possible for socialization and play, but never allowed out of sight. Food rewards may help when given after he uses his box. If he refuses to use the litterbox when confined to a small area, the confinement area should be changed to a large cage. The floor should be covered with litter, forcing him to use it for elimination. The litter is gradually removed and replaced with a litterbox. Once he has used the litterbox in a confined area for an appropriate amount of time, he can be allowed to have more freedom in the home. Previously soiled areas can be safeguarded by changing the behavioral function of the area by placing food bowls, cat bedding or toys in the area. The area can also be made unacceptable for him by placing a motion-activated alarm or lemon-scented room deodorant in the area. Plastic carpet runners can be placed upside down with the "feet" facing up. Plastic, foil, or double-stick carpet tape can be used to protect specific areas. Removing urine and stool odor is important. Products such as Nature's Miracle which are specifically formulated to work on these types of odors are recommended.
Cognitive dysfunction is a diffiult to address in cat as it is in humans. Retraining such a patient may be impossible and so confinement to an area of your choice may be the most expedient manner in which to address his inappropriate eliminative behavior.
For completeness sake, I'm going to post one of the most thorough and informative articles I know of for your perusal. Please take your time reading it and then return to our conversation with further questions or concerns if you wish.