Yes, it would be a thoughtful and kind gesture to wish someone a happy birthday, even if you have stopped talking. Taking the time to acknowledge their special day can show that you still care about their well-being and that you hold no ill feelings despite any past disagreements or issues.
Sending a simple birthday message can be a way to extend an olive branch, offering a chance to re-establish communication if both parties are open to it. However, it's essential to be sincere in your wishes and not expect anything in return. Keep the message positive and light, without bringing up past conflicts or trying to force a conversation.
Remember, it's okay if the other person doesn't respond or if they choose not to rekindle the relationship at this time. Your good intentions and kind gesture are what matter most, and it can bring a sense of closure and positivity to both of you, regardless of the outcome.