Firstly, congratulations for taking on a 'Golden Oldie'! they are often the best rescue dogs in my opinion wanting little more than a warm and cosy place to sleep and some company.
When looking at 'accidents' in older dogs, it's important to understand the possible reasons why they might be toileting in the house. Many haven't had the right home and have never been fully house trained. Others may be stressed or suffering with a separation related problem and some might have an un-diagnosed medical condition.
It's important to take these into account when looking at toilet training an older rescue dog by looking at the situations they are toileting in. Are they going at random? Are they hiding when they do it? Is it only when you go out or only overnight? Is it in their sleep? If after a few days or weeks of consistent training your dog is still having accidents, talk to you vet about possible medical reasons or a possible referral to a qualified animal behaviourist in your area, in case it's a behaviour problem rather than a training issue.
It's important to understand the possible reasons why they might be toileting in the house.
If your dog has been having accidents it's important that the soiled areas are cleaned thoroughly prior to starting any training. This is to remove an odour from your house as a lingering odour is likely to inspire a repeat performance. A solution of warm water and biological washing power, or an enzyme based cleaner from your vet are very effective at removing any lingering smell.
When it comes to toilet training – as with any training – the age of the dog doesn't really matter. What is important is how you teach them and the methods you use. Rather than trying to stop or punish unwanted behaviours, focus on what you want the animal to do and teach them that this behaviour is a great thing to do and highly rewarding. For dogs, food is often the best motivator, along with toys and praise, and is an effective way to let them know that they have done the right thing.
If you want your dog to toilet outside or in a specific area, take them to that place every couple of hours. Stay with them, watch, and wait for them do something for 5-10 minutes. Often they just sniff around or look at you wondering why you're both outside in the rain, which can be frustrating, but it's worth it in the long run. If they don't do anything go back inside and try again in about 30 minutes, keeping a close eye on them. Many dogs will start to sniff or circle prior to going to the toilet, if you spot these behaviours quickly take them back outside. Eventually they will do something outside and when they do, have a mini party and reward them for doing so with an awesome treat. Over time they will realise that good stuff happens when they 'toilet' outside and nothing happens inside.
Consistency is key for all training and toilet training is no different. The are certain times where your dog is going to be more likely to need the toilet than others, such as first thing in the morning, last thing at night, after meals and periods of excitability. We can use these to our advantage and build off them, creating a consistent routine for your dog to follow. A daily routine might look like: get up - let the dog out; get ready, have breakfast - let the dog out; (insert random daytime activity) - let the dog out; tea time - let the dog out; (evening activity) - let the dog out; getting ready for bed - let the dog out.
Lastly, it can be very effective to teach your dog a cue word during toilet training, so when you let them out they understand it's a toilet break rather than play time. This is a very useful cue to have, especially if you need to go out or are driving long distances and just need your dog to have a toilet stop. Knowing you can ask your dog to toilet on cue can save a lot of time and hassle.
We all like a reward boost every now and then!To teach it, think of a word or phrase you don't mind using in public, I personally use "be clean". When you see your dog squatting say the word, then treat when they've finished and repeat. After a few repetitions your dog will associate the word and the behaviour. You can then ask them to 'perform' and, when they do, treat and repeat. For most dogs it doesn't take long for them to understand that when you say this word and they go to the toilet, they get a treat. Once they are toileting reliably where and when you want them to you can start to reduce your treats. By reliably I mean over 80% of the time you ask them, as a minimum standard.
However, don't stop completely, we all like a reward boost every now and then!
Congratulations on your new addition. I am no expert but have personal experience that works for me. Take him or her out after meals, naps, before bed and when he or she first wakes up. Watch and you will learn your dogs signs that it needs to go. Heightened sniffing about, a sense of urgency or whining are some pretty easy signs. Also if you are gone for extended periods crate training is a good thing. Do some reading about the benefits and how to properly go about it. No matter how young or old, dogs are eager learners. Don't forget to praise him or her when they go outside. I mean really praise them even if you look the fool to bypassing eyes.