Swift generic function call underlying method based on generic type

I am writing an interface to Someone Else's Code (SEC), and I have a long list of functions more or less like this:

public func readString(_ row: Row, columnName: String) -> String? {
    return SEC.getString(row, columnName)
}

public func readInt(_ row: Row, columnName: String) -> Int? {
    return SEC.getInt(row, columnName)
}

And so on.

What I would like to do is have a single function:

public func read<T>(_ row: Row, columnName: String) -> T? {
    // call correct SEC.get* method
}

I tried a simple switch statement on T and on T.Type, but no dice. I also tried a modified version of the above:

public func read<T: ReadableType>(_ row: Row, columnName: String) -> T? {
    let getter = T.getterMethod
    return getter(row, columnName)
}

Where I could create an enum of the metatypes that had SEC.get* functions, and extend it to return the proper getter method. This to me seemed ideal. Alas:

public enum ReadableTypes {
    case String.Type       // nope
    case Int.self          // also nope
}

I'm not sure what else to try; it's not the end of the world if I simply have a dozen read* methods, but the code that calls this method could be so dang tight if I could make it generic.