Comma separated string to generic list

I was able to convert comma separated string to an IList<int> but how can I modify the same to get IList<T> where T will be passed as one of the input parameter?

i.e if I need IList<int> I will pass "int" as parameter, if I need IList<string> I will pass "string" as parameter.

My idea is to get the type whether it is int or string through input parameter and use reflection and convert the string to respective list

Code to convert comma separated string as IList<int>

public static IList<int> SplitStringUsing(this string source, string seperator =",")
{
     return source.Split(Convert.ToChar(seperator))
                  .Select(x => x.Trim())
                  .Where(x => !string.IsNullOrWhiteSpace(x))
                  .Select(int.Parse).ToList();
}

PS: Above code isn't tested yet