I don't tend to think of my inner voice/conscience as being God speaking to me. However, I do think there have been a few times in my life that I'd say God was "calling" me to something. It was an inner voice that just wouldn't go away.
The first was when I finally decided to be baptized. In my church tradition, baptism is highly valued and is seen as the mark of salvation. Tons of people will make this decision/commitment in their teen years. There were a lot of things about how it was taught that just didn't make sense to me, so I got all the way through my church youth group years without being baptized. At my church, we take communion every week (which is heavily linked with baptism in my church tradition) and a lot of sermons would end with an invitation for anyone to come down front who wanted to be baptized. During both those portions of the worship service each week for about a year, I felt like every eye in the auditorium was on me. It was extremely uncomfortable. Of course, nobody was actually looking at me, but it was like a voice was screaming at me, "Good grief, just get baptized already!" My stubbornness fought that voice for a long time until I finally decided to be baptized.
The second scenario was related to a constant voice in me saying that I should confess my porn addiction to my wife. I fought that voice even longer than the baptism voice, for obvious reasons. That was probably a few years from the point of "the voice" starting until I finally told her. Soon after, a couple of my guy friends shared their experiences and we had a small group of men who tried to be accountable to each other. The confession and finally obeying that voice was temporarily very helpful to me. However, it was the start of a very difficult time for my wife. It was a strain on our marriage for a while.
Lastly, a few years ago, I binged 200+ episodes of a podcast that was recommended to me which resulted in actually being interested in reading and studying the Bible for the first time in my life. I quickly recognized a voice repeatedly saying that I need to do something with what I learned and have been teaching classes at my church and have continued my own learning. I was nervous about becoming a teacher, but this time I didn't ignore that calling for very long. Within a few weeks of the idea popping into my mind, I was meeting with one of my preachers to discuss this journey and how to share it with others.
I look at those three instances as God talking to me is some way; a "calling" so to speak. There was no bright light. The voice in my head didn't sound different than my own voice. It was just a voice that I couldn't escape. The first was to commit myself to God through baptism. The second was to deal with my sin and the damage it causes in my relationships (still working on that 20+ years since confessing). The third was to help others start their journey to find a more loving God than the one they might have heard about so that they can become more loving themselves.
I'd like to be better at acting quickly on this voice/conscience. So many times I see a person who is obviously in need and I don't offer to help. At times, I have gone back to where that person was to offer help after thinking about it (sometimes even just a few minutes later) and I can't find them.