I think it's important to note that the runner and chaser stage can happen in any soul connection and not just twin flames, so the runner and chaser dynamic is not a specific sign of a twin flame connection.
Some people say that it can't be a twin flame connection if they are running away but that is simply not true - twin flames are the direct mirror of self and therefore carry the most intimidating lessons about facing the self. It is natural for many (not all) twin flame connections to go through this stage.
Typically, it is the masculine energy that is classed as the runner and the feminine the chaser. But they can both switch roles and in truth both the runner twin flame and the chaser twin flame are in fact runners. The runner twin flame runs from the connection and the emotions and from self, and the chaser twin flame runs from self healing by expecting the other to fill in their voids. Both are running from healing themselves.
It's important to note that mostly this is an unconscious pattern on the part of both the runner and chaser twin flames. It is part of the twin flame's lessons to bring their unconscious patterns into conscious awareness and then they can stop the cycle and make a lot of progress in doing so.
It is easy to get caught up in the victim mode and take it very personally when your twin flame is running from you, but really, they are running from themselves. They are running from feeling their emotions because any intense emotion, whether love or fear, will bring up past emotions which haven't been processed. The masculine in particular will be very afraid of opening that can of worms because they often find it difficult to process their emotions in general. There is a fear that the intense emotions will overwhelm them and sweep them away into destruction. So the runner twin flame (and the chaser) avoids looknig inwards and feeling their emotions at all costs. The chaser often focusses on blaming the runner in an attempt to avoid taking responsibility for looking within and creating their own happiness.
Runners are running away from what they see reflected back at themselves through you. They run because they worry that they cannot heal themselves, cannot change, that they will fail, that they do not deserve love. Running can be described at a refusal to communicate effectively or at all, hot and cold behaviour, keeping the chaser at arms length, cutting all ties, denying there is a connection, pushing you away out of self-sabotage, acting appaulingly to make you becoem the runner, staying in safe relationships with others, being consumed with addictions to distract them etc.
But there is hope. Twin flame runners are running through ego fears. But twin flame connections force a person to come into their soul consciousness no matter how much they try and fight it. Eventually, because the soul is infinitely stronger than the ego, they will be too exhausted to fight their higher self which is bringing them into their truth. There will come a stage when the ego will no longer be strong enough to have control and the higher self will take over the steering. This will be the stage when the runner feels that running from self is just too tiring and they will be sick of living in their fears and illusions. The fears will become a burden and they will feel strongly pulled to let go of this heavy baggage.
When a chaser is running after the runner twin flame, it only makes the runner run more because they are trying to force the runner to face themselves before they are ready. Also, the chaser is full of fear which is a dense energy and is an illusions, therefore it is pushing the runner away because reunion cannot happen in such a low vibration. Often chaser twin flames are running from facing their pain from past abandonment issues. The runner twin flame is running also from being abandonned because they fear history repeating itself from their own past.
Chaser twin flames can be very demanding, critical, intense, clingy and this only serves to make the runner twin flame feels as though they are expected to fill a bottomless pit which they cannot fill. A runner twin flame cannot make a chaser twin flame whole if the chaser (or the runner) is not whole within themselves first.
The roles can switch and then the balance gets reversed. Either way, as long as the twin flames are engaging in these unhealthy behaviours, the balance is always skewed one way of another. They are out of balance, out of harmony. This is when twin flames describe the rollercoaster. But you can get off this ride. You can observe your own role in this and put a stop to it Then your twin flame will be forced to reflect that balance back to you.
So what do you do as a chaser? Let your runner twin flame run! Give them the space they need to exhaust themselves off their own bakc and not because of you. Let them have the space to realise they are unhappy because of themselves and not because of your "nagging" or "clinging". It could take years before they truly awaken, but if that is the case, then that is what the universe has planned and there needs to be an acceptance of that. Everything happens the way it should.
Your higher self wants you to step off the rollercoaster and spend this time looking deeply within yourself, because chasers have a lot to heal too. Many chasers mistakenly think it's only the runner who needs to heal.
There is no need to run or to chaser in your twin flame connection. You are supposed to reconnect with yourself, love yourself and create that wholeness within. Your raising vibration will travel through your merged chakras and cause your twin flame to raise in vibration automatically. However, you need to raise your vibration for your own sake and not just to be with your twin flame. The universe will know if you are only trying to achieve a higher vibration just to get your twin flame back to fill in voids. Do it for yourself, yourself truly comes first.