Everyone has their favourite techniques. I like ojikaeshi do and suriage men. One works against taller opponents and the other is useful against players of the same height or less. I find though, that if you rely on a limited number of techniques, you are easy to read and a skilled opponent will instantly be on his guard. So there is a conflict between the need to polish your best techniques and insure you have a varied selection of techniques to work with.
I was taught that to learn a technique you should practise it exclusively for three months. The way I understand this is that you should concentrate primarily on the waza that you wish to master during your kihon practice and to use it as much as possible in jigeiko, but not to the extent that your dojo mates become totally bored.
To be frank, It is much easier to concentrate on a specific technique if you are the senior party in jigeiko. You can decide on a technique that you will attempt a certain number of times in each practice with your juniors as a form of yakusoku-geiko. This is not possible when you are evenly matched or outclassed. When you stretch to become a useful opponent for senior kenshi , you have to give it 100 per cent; attacking any target that presents itself as soon as you see the opportunity.
When should you start to “make it your own”? I am not sure. If you start too early, you are in danger of ingraining bad habits. If you never find a technique that you prefer to all others, you have either reached a level of munen mushin that many martial artists aspire to throughout their lives, or you simply have not got anything to work for you well enough to concentrate on it as a speciality.
The logical way forward is to practice all the techniques that are taught to you. If and when you find something that is particularly effective; then experiment with it. Try techniques against shorter and taller opponents, younger faster and older more experienced players, when you find something that works start to polish it.
The first of the shogo titles, Renshi, means amongst other things, polished person. Polished in this case applies to the whole person, not just to particular techniques that they are good at. However in Japanese practising and polishing can have the same meaning and as the old British proverb has it “practise makes perfect”.
Train to perfect your tokui waza, then put it away. Hide it until the opportunity to make the decisive strike presents itself and then just let it out.